One of my recent visitors was looking to learn how to realize figured bass.
Figured bass is a way of notating harmonic progressions without spelling out all of the notes of each chord. It is Old School lead sheet notation. The bass line is given, with some numbers (figures) written under some of the notes. Here are the rules:
1) If there are no figures under the note, the chord is a root position triad.*
2) 6 by itself under a note indicates a first-inversion triad.
3) 6/4 indicates a second inversion triad.
4) 7 is a root position seventh chord.
5) 6/5/3, 6/4/3, and 6/4/2 are the first-, second-, and third-inversion seventh chords respectively.
6) Because scribes were lazy, the previous figures are usually shortened to 6/5, 4/3, and 4/2 (or just 2).
7) An accidental sitting by itself (# or b) alters the third above the bass. NOT the third of the chord (necessarily), but the note that is a third (plus octaves) above the bass note.
8) A slash through a number is the same as writing a sharp before the number: raise the referred note by a half-step.
There are many more rules about suspensions and the like, but that gets the basics. Now, how to put it in practice. First, play the bass line solely with the left hand, and leave all other notes to the right hand. Second, keep your right hand from leaping around the keyboard. Properly realized figured-basses have very smooth (i.e. stepwise) motion in the upper voices. So, grab any convenient notes for the first chord, and look for the closest possible notes for the next chord. Continue until you reach a cadence, then reset. When possible, move the right hand contrary to the left hand (this helps avoid parallel fifths and octaves).
This advice does not guarantee a flawless realization, but it will produce a convincing realization. If the above is too simple, the next steps are to consider tendency tones: the leading tone Ti and the chordal seventh. These notes must never be doubled, and must resolve the way they intend (up and down respectively). Speaking of doubling, root position triads double the root, first inversion triads generally double the soprano, and second inversion triads always double the bass. But again, these rules need to be heeded for a polished performance, but not for a rudimentary performance.
Above all, keep the rhythm! If you aren't sure what chord to go to next, fake it. If you are afraid you will play parallels, go ahead and play them anyway. Performances are not perfect.
* Hard-core keyboardists know that many old figured-bass scores do not include all of the figures. The scribes figured that EVERYONE knows a Do-Re-Mi must be I - viio6- I6, so the 6's would be omitted.