ArchBass -
Hi, and welcome to TalkBass.
This is a pretty involved subject, but I'll try to be brief.
A good deal of Erick's advice is on the money, particularly the thing about placing your finger directly behind the fret. As Erick mentions, this will make it easier to press the string to the fret and get solid contact, getting the best tone for the least effort. Also, he's correct that playing with one finger per fret isn't mandatory. I generally don't myself, instead using the exact technique that Erick described, borrowed from upright players. But, I also spend a great deal of time PRACTICING with one finger per fret technique, because when you need it, you NEED IT, and if you're not prepared, it'll be tough to pull off. I'd go into the right hand muting stuff, but that's a whole 'nother post, suffice it to say he's right there too, very important (I believe if you do a search, you'll find a thread on that topic).
As for your over-all left hand technique, well, it starts at your SHOULDER, not your hand. It's easy to get caught up in what your fingers are doing and not pay attention to the whole picture. Make sure you are standing or sitting with good posture: back straight, shoulders back. Hunching over will make it harder to play and could eventually lead to back problems, it will also make you tire quicker.
The next thing to be aware of is where the bass is when you play. I personally am a STRONG proponent of having the bass moderately high on a strap, and always practicing that way. I have my bass hanging in the middle of my chest, but anywhere ABOVE the waist (meaning the whole bass) is good The main reason for this is to make it easy on your left hand. Another component of this is the angle which you hold it at, which should be approximately 45 degrees from horizontal.
Here's a couple photos of me playing, to give you an idea of how I hold my bass (it may give you some other pointers as well):
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Now to your arm. It should be relaxed, upper arm going almost straight down, with a slight seperation from your body, to the elbow. Then just reach up, and place your thumb on the center of the back of the neck, pointing towards the ceiling. Your arm should be almost loose, pivoting between your shoulder and your thumb. As you move across the string, you should gently rock your arm forward as you go to lower strings, or back as you go to higher strings.
Next to the fingers themselves. Your description of "cupping" is good, you should position your fingers so that the tips of them USUALLY are what make contact with the strings. There are certain times that will call for a different technique, but I'm not going to cover that now.
But, there is one exception, in my opinion: I don't keep my first finger curved or cupped, instead it's somewhat flatter than the other 3, which allows me to use it to mute the strings under it. I also tend to use the very tip of that finger to mute the string above it at times.
The thumb, which I already mentioned should be generally in the center of the neck and pointing at the ceiling (remember this is GENERALLY, there are always exceptions to the "rule"). You should have the thumb extended fully, but not be forcing it to be extended, a "relaxed extension" would be a good way to put it, sort of like a "thumbs up" or hitchiker's thumb. DO NOT point the tip of the thumb at the neck. You should have the thumb positioned APPROXIMATELY even with where your second finger is on the fingerboard, or slightly towards the first from that place. As you move across the strings (with your arm moving forward and back from the shoulder), your thumb should roll across it's pad. When you're on your higher strings, it should be near it's tip (but of course never ON it), and when you're on your lower strings, near the first joint of the thumb. This is all going to be accurate for lower positions, I find that as I tend up the neck, my thumb starts to point slightly towards the headstock of the bass.
Hope this answered a few questions and was helpful. Bet your also hoping the next time that I don't decide to be long winded, eh?
[Edited by Gard on 01-16-2001 at 09:25 AM]