In terms of arranging, be bold. You could obviously just go with the typical Head, Solos, Head "form," but my combo has received a lot of credit for the interesting arrangements we do. It's hard to do in a trio, but you can do a lot by limiting certain sections to a certain portion of the combo. You can also write cool riffs/licks to insert during, say, a drum solo or bass solo. There is a lot of showmanship to be had with small group jazz, because it's not as difficult to stick together as in, say, a big band or a 9-piece group.
As for writing songs, start with a modal approach. Learn II-V-I chord changes and the modes of a scale (for a C scale, the ionian scale would begin/end on C, the dorian on D, phrygian would be E, lydian F, mixolydian G, aeolian A, lochrian B and then you're back at C an octave above). Most of the jazz that works in a trio is based off modal chords (which are essentially just changes that are based around a single key signature, allowing soloists greater melodic freedom during improv sections), for example, the entire album, "Kind of Blue," by Miles Davis is modal jazz.
You can do some Wikipedia searches and get most of the info necessary to start experimenting with this stuff... or you could just ask your pianist, they'll probably be able to explain it all much more efficiently than I just did.