Hello all. I'm a beginner who just obtained his first bass one week ago. I have no bass teacher so I have to try learning myself and I have one critical question: what is the best way to play two notes consecutively on the same fret on two different strings? For example, you have to play C and immediately after you have to play F. What is the best technique for that: is it better to use the same finger of the left hand, or two different fingers?
Thank you very much. Sorry, the answer may be obvious for you but I'm just beginning.
I think some of the responses here may be a bit confusing. I'll assume you're right handed, and your question is about the fretting (left) hand. In most all cases, you would use the same fretting finger for both notes. The method to use, as a few have noted, is by rolling your finger between the two strings. The exception to this would be if the passage forces you to move positions up or down the neck, which might be helped by using a different fretting finger, or if the passage is so simple that alternating two fingers is just easier.
Furthermore, if your bass has a relatively thin neck (Jazz-sized, or 1.5" measured at the nut) the finger roll is relatively straightforward. But for necks that are larger than that, or if you are jumping two strings (say, that same C at the third fret on the A string followed by a Bb at the third fret on the G string), you may have to quickly shift your fretting finger from one note to the next - or, again depending on the musical passage, you may be able to use a different fretting finger. Since there are many times when you'll need to use the same finger, the only way you'll gain the dexterity to do this well is through repetition.
And since you're so new to bass and don't have a teacher yet, try to keep your fingers nominally spaced at one per fret, with the fingers relatively parallel to the frets, your thumb pointing to the ceiling, and keeping your fingers close to the strings. These are general guidelines but will serve you well; it'll be bad if you practice some things over and over with poor technique.
Some of the responses here (Germanson in particular) address the plucking, or right hand. As a beginner, you should do your best to alternate plucking fingers as much as possible. After you get some time on bass, you'll learn that there are times when it is easier/better to not do so; but for the time being, becoming proficient at alternating plucking fingers will pay huge dividends down the road (and later you can worry about rest strokes and comb strokes and whatever else).
Finally a quick note about muting. As a general rule (it may or may not be called the floating thumb technique, but) if you maintain your plucking hand's thumb on the string below (the one thicker) the string you're plucking, you will mute that lower string; your left (fretting) fingers will naturally mute the higher (thinner) strings. (The actual "floating thumb" technique, as I gather from Todd Johnson's forum here, involves laying your plucking hand's thumb across the strings - very effective technique, but something I never took the time to become comfortable with). When playing with a pick, it is generally best to use your right palm to do a good deal of muting.
Hope this helps, and welcome to the low end.