How would I play a song in all righthand chords? Would i just play all the melody notes as chords? (My instructor used to do it, he would say it leaves the LH free to do other things)
Usually this technique allows you to add musical interest by filling out the left hand with more harmonies or a counter melody.
You'll want to keep the melody in its own musical space - so either play it with the top of the right hand or the bottom of the left hand.
To keep the melody on top, build the chords with the melody notes at the top of the chord, and try to leave a space (>3rd) to the next note. You'll probably have to leave a note out of the chord to accomplish this, probably you'll want to lose the fifth, but that may vary between chords. Follow standard voice leading rules. This leaves the left hand totally free to do an independent voice like a walking bass, or you can use it to fill out the rhythm line. You can also help the melody stand out by playing it on the beat and the chords off the beat.
To put the melody in the lowest part, you'll want to probably play it in octaves with the left hand and keep any other voices >5th away. The right hand can play the same chords as the left normally would, but generally these are broken into a more virtuosic pattern.
In any case, this is best executed by someone with fairly advanced technique, but it can also be helpful for building left hand independence.