it partially depends on which harmonic language you are working with.
Some types of harmony lend themselves well to certain motivic treatment, while others less-so.
In common-practice harmony, you might consider high and low points of a motif (the upper and lower limits) and then consider how those might be modified, either by sharpening or flatening, to allow new harmonizations of the same motif.
If you have a motif that lends itself well to it, you can also "expand" on it horizonatally. A four note motif (for example) can be repeated verbatim. However, you can also modify the repetition in a number of ways.
You could alter the intervals of the motif but so that the contour remains identifiable
You could alter the rhythm so that the repetition either lengthens or shortens the over-all motivic repetition.
You could repeat a fragment of your motif, for example the head (first notes) or tail of the motif.
The repetition of fragmentary material could be altered as in 1. and 2. above
You could lengthen the motif through "growth" of the material. If the motif has 4 notes, then the repetition might have 5 or 6, then 7 or 8, etc... until a lengthy "theme" grows out of it.
In a less "tonal" medium, a motif can be used to create inversions and transpositions of itself. Simply repeat the notes of the initial motif, using the actual notes of the original as "launching points" for the repetitions. This is a good way of creating "related" harmony without relying on common practice notions.
Motivic material can be mirrored, inverted, retrograded, like a tone row.
If a motif has a characteristic interval in it - a leap, for example - that leap might be inverted to create a completely new "version" of your material. Instead of leaping "up", you might transpose that leap down an octave. While technically moving to the "same" note in a different octave, it still creates a sense of newness through the difference in register.
A leap might be used where none was present before (a much more "shocking" effect). If you have a motif that is mainly stepwise motion, then repeating it and suddenly moving one of those steps to a different octave can create a sense of drama.
let me add one more detail, but a pretty important one:
Avoid motifs that are "complete".
In other words, a motif that starts and ends on a solidly "tonic" note is considerably harder to develop, as it has a tendency to feel "complete" in and of itself.
I would say that the major difference between a "theme" and a "motif" is that the motif is incomplete on its own, while a theme has a sense of direction to a climactic point and back from it.
Creating a motif that is harmonized as I - V - I can be extremely limiting. While creating a motif that ends in harmonic suspension or ambiguity leaves the door wide open. The audience's ear does not know where it is headed and it gives you considerably more freedom to move into new harmonic territory.
There are the standard variations that work with themes or motives:
Transposition: in non common-practice harmony this is direct, in other words C Eb F tranposed up a minor third is Eb Gb Ab, whereas in traditional it would transpose based on the scale unless a modulation or modal modulation is occuring.
Inversion, same as above. C Eb F inverted, but still starting on C would be C A G in non-tonal, C Ab G in tonal.
Retrograde. Motive backwards.
A combination of the above.
Motives can also be rhythmic. So any pitches can be used as long as the rhythm is the same. One can double or half that rhythm as a whole alse and it will still be heard as derived from the motive.
If you want a FANTASTIC example of motives, curl up with scores to Beethoven's 5th, Pathetique Piano Sonata, and the Eroica. They are pretty obvious and easy to follow. When you get good at analyzing those, move on to others. This is always the best method to discover how composers do things.
My idea of the term is that a motive is the smallest piece. With motives one can create themes. Beethoven used the four-note motive in the 5th Symphony, but it was used to create the entire first theme. Another compositional tool is the leitmotif. Wagner was the quintessential master of this. It is usually slightly longer than a motive, but sorter than a theme. It can consist of a combination of melody, harmony, and/or rhythm. He would set these to specific characters, moods, or events. After the audience hears them a number of times they come to ascribe these in their heads as being related to what the composer intended. John Williams and film composers use them often too. They are usually restricted to opera or film scores, but programmatic composers use the idea in their works. (see the idee fixe in Berlioz's Symphonie Fantastique)
DMA Student and Teaching Asst in Music Theory/ Composition at the University of Miami Personal Website