I feel like it's a universal desire. Everyone seems to want to play guitar at some point or another. I definitely did. I was thirteen years old and a friend of mine was telling me how his dad just bought a couple of guitars and an amp so they could play together. I was invited over just to mess around with them because neither of us really knew how to play. We were in a dark, dingy basement trying to figure out how to play nirvana songs when Bob, the father, showed up and said "Let's jam. It'll be fun. I'll show you guys what to do." They only had 2 guitars but he brought a bass guitar in with him and asked if I've ever played before. Of course I hadn't, so I told him, "Nope." He assured me it'd be a piece of cake. I slung the bass over my shoulder and right then I got my first bass lesson.
Bob told me we were going to play a blues progression, also known as a 1-4-5. It's called 1-4-5 because it consists of 3 chords, each starting at those locations on the scale, so if you're playing an F blues, the chords would be F, Bb and C. This probably won't mean a lot to you right now but the genius part of guitars is that you don't really need to know these things to get started. What you need to know is that it's the big string, first fret, second string first fret and second string 3rd fret. I of course only knew of strings and frets and was shown a very simple pattern that I could move to anywhere on the neck and have it work. I played the bass, my friend strummed the chords and Bob soloed over us for a good 30 minutes. We were a regular blues band.
The nuts and bolts of a bass guitar
The way any guitar works is by vibrating a string at a certain length. The shorter the length, the higher the pitch. You change the length by pressing on the string right before, but not on, a fret. The frets are the little metal bands that are all over the neck of the guitar. The 12th fret of a guitar is the exact halfway point from the bridge down at the bottom and the nut up at the top near the tuners. It is also also 1 full octave above an open string position.
A standard bass guitar has 4 strings: E, A, D, G in order of lowest (thickest) to highest (thinnest). Each string up is exactly 5 frets higher in pitch than the last. This means that if you play the 5th fret on the E string, it will match pitch with an open pitch on the A string, because that's A. Conversely, the 7th fret on the A string is exactly one octave above open on the E string, because 7+5=12 and 12 half-steps is an octave. This also works to make an octave if you play the 2nd fret on the D string and open on the E string, because 5+5+2=12. None of this knowledge does you any good, however, if your instrument is not tuned!
Tuning a bass guitar
A guitar does not have to be in perfect tune with the rest of the world to work correctly (A = 440hz) , just itself. There are a few good reasons to tune it to the correct pitch, though: The string tension & resulting action (distance from the string to the fret, check the section on truss rods and bridge adjustment later) will be more correct, you can play along with other instruments and you can play along with some recordings (provided they're tuned correctly as well).
Start by matching one of the strings with a known tuned pitch, such as a tuner, piano or another guitar. If you've got a good sense of pitch or are used to hearing intonation (the difference between two pitches) you should be able to get it lined up. The trick is to get rid of the intonation, which sounds like the pitch oscillating up and down. The faster it goes, the farther off you are. The slower, the closer you are to having a good match. I recommend tuning the A string first instead of E. I find it easier to match up with other instruments and it usually holds its tune better while changing the other strings simply due to its tension.
Now tune your other strings to this string. If you tuned the A first, do the E by holding the E down on the 5th fret and playing both strings at the same time. At first you will just have to play with the E's tuner until you get close then keep plucking and listening very closely for intonation until you make it go away. To do the D string, hold the 5th fret on the A and repeat using the D's tuner. After the D is in good tune, hold the 5th fret on it and finish off by tuning the top string.
You can cross-check the tuning of the strings by checking octaves via a bottom open string and the next string up on the 7th fret. It should sound clear and not wavery (intonation). If the bass hasn't been played before, there's a chance the bridge needs adjustment but for now don't assume it does.
For more help, check the bass guitar section of Get-Tuned
How to physically play
This is for right-handed people. If you're left-handed, do everything the opposite of how I'm explaining.
Hold the bass either in your lap resting on your right leg or standing with a strap over your shoulder. If you're using a strap, don't let it go too low. I know it looks cool, but basses are really hard to play when held down too low. Somewhere near your stomach should be a good spot. Some experts say the higher the better but I find that unnecessary. Just make sure you still have a comfortable bend in your elbow when holding on to the strings with your right hand.
Your left hand should feel free to move over the neck, with the thumb bent back a bit, anchoring the hand against the back of the neck. You should be able to press down on a fret (not actually on it, but about a half inch behind) without too much effort. With your right hand, at first you will want to push your thumb down against a pick-up (the little electronic things under the strings) so that you can use your pointer finger to pluck the string. Eventually you can anchor your thumb against the bottom string until you need to hit that string in which case you bring your hand off of it. Don't worry about that now. Just get your hand comfortable and pluck with your pointer finger while holding the fret with a finger on your left hand. That's the basic technique. You can also use a pick with your right hand. It doesn't matter. Do whichever you prefer.
Start with something fun
I've seen teachers try to go immediately into scales, theory, technique, drills and anything else you can think of. Guess what? People respond the best to something that's instantly rewarding, and those certainly aren't. Pick a simple song that you're inspired to play. It can't be hard and you have to like it. There are plenty of good songs like that. If you have a friend who can play, ask them to learn it and show it to you. It may be 3 notes. It may be something that slides up and down a few spots on the neck. It doesn't matter. The most important thing is to have a few easy fun things that you can play right away. If you don't have a friend that can show you, listen to the song several times and experiment plucking notes out that sound about right. That's what people refer to as "playing by ear." You should be able to pick up the song fairly quickly. This is the first thing you should play and you'll be able to play it for yourself your very first day! From now on, any time you try to learn something that's a little too hard and you get frustrated, just come back to one of these songs for a few minutes to relax. You'll be glad you did.
Build your muscle memory
From this point on there are several ways to improve your skills, but no matter what, the key is going to be lots of practice! The more time you put into it, the better you will get, period. I was so into it when I started that I played about 3 hours per day for about 6 months solid. I went from being able to play almost nothing to being able to play 99% of Primus songs very well, which, even if you're not into Primus, is quite an achievement for a bass guitar player.
I picked two methods of getting better. One was to take a few bands that had very challenging basslines and make myself learn them and the other was to practice a few different finger agility techniques daily. I found both of these methods to be very complimenting to each other and important to developing my skills. Picking difficult songs is fairly straightforward, but often times even figuring out what they're doing, much less replicating it yourself seems near impossible. I found that reading through tablatures online, buying tab books and especially videos of them performing is extremely helpful. Finger techniques are much more established.
One of the best drills I learned is what I call a four finger walk up the neck. The way to do it is to start with your first finger on fret 1, second on fret 2, third on fret 3 and fourth on fret 4. You play each fret with the respective finger, then slide the whole position up on fret and repeat. Your right hand technique can be single-finger plucking when you're just getting started or you can alternate with your pointer finger and middle finger when you're getting more comfortable. This is the preferred way to play faster. You repeat this until you're up to the 12th fret, then reverse the exercise to take it back down to the 1st fret. This exercise not only builds muscle memory and dexterity, but also is the most helpful one I've found in developing tight coordination between your hands.
To play slap/funk style, I just practiced hitting my thumb on the bottom string and pulling an octave on any higher string. Eventually just playing around with that, you'll start to find ways to play things that you've heard other people playing. I've found that more with slapping and popping than anything else it's all about experimentation. Get fast with the thumb, which really means get a fast twitch developed with the turn of the wrist. It takes a lot of practice, but eventually you'll get quick and will be able to make some very percussive noises with just your hands.
Beyond just mimicking
Given what I've explained so far, with enough time and practice you'll be able to mimic anyone's song. This is great until you want to start modifying or writing your own bass-lines. I'm not going to get into any music theory in this article, but I will give you a few more exercises that will help you along with this.
First you will want to learn a couple of basic scales. You should be able to find tabs for them online. The major scale is first on the list, followed by the minor. Those will cover 90% of cases. Practice just walking up and down those scales on every position on the neck (eg, start with E major, then F major, then F# major, etc..). After hitting the top, do the same all the way back down to the bottom. The first time it will take quite a while to complete this, but once you're playing faster, you should be able to do it in a minute or so. Repeat the same exercise but with the minor scale. What you're trying to do with these is memorize what the scale "feels" like to play, so that when you're given just a chord for a song, you know what notes work without having to think much about it.
After getting the straight up and down scales down, the next good exercise is alternating every other note. By this, I mean playing notes 1,3,2,4,3,5,4,6,5,7,6,8,7,9,8 in that order of the scale. Then reversing it all the way back to the bottom, moving up one half-step and repeating. Do this all the way up and all the way down the neck for all major and minor scales.
The value is in your own time and effort
What I have told you is the compilation of all lessons and teachers I have had in 13 years of playing. It's the vast majority of what is taught, and it's all things you can learn on your own just by trying. Yes, you need to know all of these things to get there quickly, however once you do know them, how good you get is really determined by how much effort you put into it. The more you put in, the more you will get out. Just remember to keep playing things you enjoy. If you're not enjoying yourself anymore, you're defeating the purpose of playing music altogether.
Wikipedia contains a good amount of general info on bass guitars here