Perhaps the simplest was is to go directly from the amp to a mixing board. This gives you some control over the sound because of the mixers equalizing capability. Doing this allows you to cut out both microphone and amp inadequacies. It also gives you a clean tone. If you are going for that clean tone you can also plug your instrument directly into the mixer or four-track. You will lose the boost character of an amp but you will still capture that “fullness” that some bass players hunger for.
You will find that compression helps a great deal with bass recording. As with the nature of compression you want to cut down on the peaks but not to the point that you spoil your attack. Play around with it.
Another method is to mike the amp as F_cksia mentioned above. A good way to do this is to place the microphone within 4-6 inches from the face of the amp. For a brighter sound point the microphone directly at the center. For a deeper or duller sound, gradually move the mike’s direction away from the center. A great spot is to point it directly at area where the speaker meets the dust cap. You have alot of room to experiment here. You can move the mike’s focus around at your heart’s content until you hit upon a sound you like.
The best of both worlds is to go for both. All this means is that you split the signal between the amp and the board and/or four track. This way you achieve the character of the amp and the full tone of going direct. You can also use a compressor here to smooth the mix out. This can be fun because you have the ability to choose which of the two sources you want to push to the front of your bass track.
There are many different styles when it comes to bass playing, and you will need to find the right method when recording it. You may find one way which works and stick with it. The last word here (as always is) to never be afraid to experiment. Try adding effect to the bass. Some players find that applying bass effects adds just the right amount of punch to the track and they stick with it.
One final thought here is what Shailat said. Unless it’s your intention, you may not want to record your bass to the point that it is so clean that it stands out in the mix. What is meant here is that if you are going for a bass solo then that’s fine, but the bass should typically lie just below the point of being intrusive. The ear will find it – it always does.

Jaymz