Some stuff- Get a teacher for the first year or so. Make her or him show you these things-
1. Proper lefthand technique. This is where most people run into problems by forming bad habits. There are so many people who are self taught that don't use their pinky, or even sometimes their ring finger, because they don't have the same finger strength as the first two fingers. This can lead to a really bad habit that's hard to correct, and that will drastically limit your playing.
There are typically two left hand techniques - one is a flathanded technique typically used by jazz guys, and the other is curled finger technique like a guitar player. Learn both; they can each be used to do different things.
Do fretting exercises that require you to use your whole hand. The easiest one is just to hold down on the first fret and, keeping your finger down, play the second fret, then the third, then the forth. Don't lift any of your fingers, it will build some strngth relatively quickly.
2. Proper right hand technique- I am firm believer in using your fingers rather than a pick. Having said that, some of my favorite bassists use a pick with great results (see e.g. The Jesus Lizard). Here's the deal- even if you want to play with a pick, learn both. It will expand what you can do with the bass.
Proper right hand technique should involve some knowledge of how to do a rest stroke. It's easy- use only your index and middle finger. Rest your thumb on the top (E) string; or, if you're playing the E, on the pickup. Alternate your fingers, and make sure each time you pluck the finger you are using rests against the string above it.
3. Learn timing. There's nothing worse than a bassplayer without rhythm. Buy a metronome and practice playing on the beat.
4. Learn the notes on the neck, and some scales and basic music theory.
5. Ask them to teach you basic styles. Even if you really, really, really want to play nothing but metal, country, blues, etc. You will be shocked how much you can learn by just learning different genres. Obviously, some rock styles are great, learn blues, some jazz, and reggae is great.
Just a warning, some teachers will only want you to learn your favorite songs form bands and that's it. That's a little like learning how to pronounce words in a foreign language, but not what the words mean. It's more improtant how song or bassline works. Once you feel you have a good handle on the instrument, drop teh teacher and start just playing. You'll develop your own techniques thatwill vary from what you've been taught, but that work for you.
Last piece of advice - play with anyone and everyone you can no matter what style. Play with people who are obviously better than you, you'll pick up so much more stuff quickly that way. Best of luck!