I hope someone with actual harpsichord experience chimes in, since most of what I'm writing here is hear-say.
As you no-doubt already know, the two main things that you lack on a harpsichord, compared to a piano, is a long sustain, and any appreciable dynamics. I've heard that one way to compensate for the lack of dynamics is to vary the duration of the note. If you hold a note for it's full duration, then it is perceived as being louder than if you play with in a more disconnected articulation. Thus articulation is not used so much a means of phrasing, as it is a means of conveying accent and meter.
This emphasis on articulation is addressed, for example, in the following PDF: Elementary Harpsichord Technique, by Roy Truby, originally published in The English Harpsichord Magazine (1975), and reproduced (with many other articles) at http://www.harpsichord.org.uk/EH/ehm.htm. It stresses playing with a more detached (non-legato) articulation, and taking care to not slur from a weak beat to a stronger beat (unless specified by the composer). OTOH, it also warns against hyper-correcting, and playing everything staccato.
Another technique for accenting notes is to use ornamentation (trills, mordents, and the like), which was a very important aspect of Baroque keyboard music, about which, much has been written. Trills can also help with sustained notes, since you'll often find a trill placed over a long note, so as to sustain the sound from that note.
For larger sections of dynamic (and tonal) contrast, some harpsichord are endowed with alternate stops or registers -- differing sets of strings, with different tonal qualities, which can be played, either individually, or sometimes coupled. Perhaps the most recognizable of these is "Lute Stop", which has a very thin, veiled sound, like a lute (hence the name). By some accounts, this affect was much-loved by Bach.
Another effect, which you probably can't get on a digital piano (unless it has fairly sophisticated acoustic modelling), is sympathetic vibration. That is, if you continue to hold a key down, even after it's sound has died away, the string will still be able to vibrate whenever it shares a common overtone with another string that's being played. This can lead to a fuller, more resonant sound. This effect happens on pianos as well, but (at least without the sustain pedal) it can be less noticeable, given the piano's greater ability to sustain notes. This is also a reason why playing in justly-tuned keys (rather than Equal Temperament) sounds better -- there are more shared overtones, leading to more resonance.
You may also want to check out the classic period text on the topic: Essay on the True Art of Playing Keyboard Instruments by C.P.E. Bach (perhaps the most famous of J.S.'s numerous children).