To be seated at a good height, the underside of the elbows wrists and fingers are level. The center of the body and that of the keyboard should coincide. One should turn very slightly to the right, the knees not pressed together, with the right foot extended. One must have an air of ease at the harpsichord (François Couperin, 1716). The elbows are a bit below the level of the keyboard, so the hands are as if glued to the keys, giving the fingers as much contact as possible (Jean-Philippe Rameau, 1725).
The wrist must always stay relaxed, and so the fingers. The movement of the fingers is entirely from where they join the hand - no large movement should be made where a smaller one will suffice. (Rameau) The movement of J.S.Bach's fingers was so slight that it could hardly be seen. Only the top joint seemed to move. His hand retained its rounded shape even in the most complex passages (Forkel, 1802)
Softness of touch requires holding the fingers as close to the keys as possible. A hand falling from high draws a harder sound from the string (Couperin). Never weight the fingers with the hand, rather the hand must support the fingers (Rameau). In running passages, fingers should not be lifted quickly, rather their tips should be drawn back to the edge and glide off it. This will make runs clear (J.J.Quantz, 1752, describing J.S.Bach).
As Couperin notes, the purest sound is made when the plectrum strokes the string rather than banging into it. In reaction to the pluck, the plectrum is kicked away from the string; in well-made jacks the axle of the plectrum is low down on the tongue so the plectrum makes a slow return to the position for a subsequent pluck. This time is sufficient for the jack to drop the plectrum below the string before it can hit it on the way down. So the finger motion is: 1. depress the key so the plectrum is just below the string, 2. stroke the string with the plectrum, then immediately 3. drop the plectrum below the string quickly enough that it doesn't contact the string. (Of course, the jack must not drop so far that the damper touches the string until the desired end of the note.) This has two desirable results: 1, when the note ends, there is no noise from the plectrum contacting the string before the damper does, and 2. when a note is repeated as in Scarlatti, or in a trill, the sound is a repeated clean pluck without the extraneous noise of the plectrum touching the string on the way down. Our 4 fingers with pads held in touch with the key can develop the required feel to flick down and up as this technique requires with steady one-finger-at-a-time practise. At speed, the motions reduce to two: 1. tap the key so that it descends to just short of where the plectrum would touch the string, 2. stroke the string then release the key in one motion (me, 1980).
When we hold our hand at the keyboard, the sensitive part of the fingers lies on the keys, but only the relatively insensitive side of the thumb. So, it is built into our hands that, when the maximum sensitivity of touch is desired, the thumb should be little used. The length of our three central fingers is greater than of the outside finger and thumb, so they are the natural fingers for accidentals.
Prior to 1700, fingering of all keyboard instruments was based on this natural shape of the hand and on systems of strong and weak fingers. A typical fingering for a right hand ascending scale would be 2-3-4-3-4, descending 4-3-2-3-2. Observe the fingerings Couperin proposes in L'art de Toucher le Clavecin for les Sylvains or les Ondes of his first book - the latter has three lines of 16th notes with the thumb used only once outside of a stasis. As for Germany, C.P.E.Bach recalled that his father grew up among great players who used their thumbs only when required for large stretches. Fingering with almost no use of the thumb must have been the norm until the 18th century in France and Germany.
It is often argued that the crossing of fingers in this way must result in a strong pairwise articulation and that the music was to sound chopped up. But, early sources rarely support fingering as interpretation, in fact a few make it unmistakeable that this was not the intention at all. For example (although a bit late):
Five fingers can only play five notes in a row. To extend this range, there are two main techniques: the turning under of the thumb and the crossing over of the fingers. Both must be done so that the tones flow smoothly. In keys with few or no accidentals, the crossing of the 3rd finger over the 4th and of the 2nd over the thumb are best suited for unbroken legato. (C.P.E.Bach, 1753).
We are all taught smooth thumb-under technique today. The key to smooth playing with finger crossovers is that the hand should point towards the key to be played next (Tomas de Santa Maria, 1565). One can make a very fluid legato by 'walking' the long fingers along the keyboard this way. Most naturally, though, it creates an articulate legato that corresponds to wind-players double-tonguing "tu-ru-tu-ru" This is not choppy-sounding, nor does it separate the passage-work into groups of 2 or 3. Rather, it creates a musical line which is speech-like. There are many early art works that show this technique. One of the most famous is reproduced here, St.Cecilia by H.Goltzius ca.1588. (It reappeared 25 years later on the title page of Parthenia, with a virginal substituted for the organ, and with no keys depressed!)
But, in 1716, Couperin notes that one must abandon completely 'the old way of fingering' to play properly. By 1724, Rameau instructs that the thumb and 5th finger must touch the edge of the keys and the other three fingers must curve so that they too touch the key edges. Every finger must have its own movement, separate from all others.
It is impossible to play many of Domenico Scarlatti's 1738 passages at anything like the speed he notates them unless the thumbs can be fully used on the naturals and passed under the fingers. Consider also passages such as those in K.24, with double 'Alberti' thirds over a pedal note in one hand that calls for an appreciable sense of touch with the thumb to play at speed without turning a harpsichord into a bass drum. Not to mention that an air of ease at the keyboard is obviously not the expectation of a society that accepts four octave leaps of one hand over the other written for a Queen! (cf. K.99) I am certain that Scarlatti played with a hand position similar to Rameau except more accomplished - the thumb firmly on the naturals, the fingers curled mostly at the second joint from the end so that they stay clear of the sharps and the maximum of nerve endings are on the keys, and all ten used to their maximum possible advantage. (A surviving painting of Scarlatti shows his left fingers in this posture, and the painter noted specially the humps of skin over the second joints of his right fingers, which are depicted only slightly curved.)
There are other techniques that I am certain Domenico Scarlatti used, that I describe in Keyboard Technique - Speed.
other notes on harpsichord playing
I thank Dale C.Carr for providing a photo of the Goltzius engraving.