I write down whichever pieces I want them to work on in an assignment folder. The number of pieces as well as how much they need to get done varies with the level and learning ability of the student. With some, I am more specific than others. Most of the time I write in sectional symbols into the score, give verbal detailed instructions, and then write an abbreviated form into their folder. At the end of the lesson, I have them say back the assignment to me.
For elementary students, I have them working out of their method books, maybe 1 or two pieces, plus a special solo piece, and after they're in level 2 or so, I start adding a scale each week, either 1 octave HT or 2 octaves HS, and then short sight-reading exercises.
Intermediate students have maybe a piece at their level, a piece easier than their level, a "pusher" piece a little harder than their level, scales (or whatever other technique I assign) and sight-reading exercises.
That's a GENERAL plan, and it changes from week to week of course.
Advanced students I am less rigid with what they are playing. I have them do solo pieces, some technique, ensemble pieces, and then things like harmonization, playing by ear, some improvisation in a limited setting (usually hymnplaying). But it is not as structured as my less-advanced students.