With a solar filter and telescope mount:
(1) Measure length of Sun's day by observing movement of sunspots.
(2) Measure angular motion of Sun across sky (setting or rising may be easiest as horizon provides fiducial mark) to get length of Earth's day.
Remove filter and observe Moon:
(3) Observe Moon's angular motion; see how it differs from Sun's angular rate to determine Moon's orbital period. Support with photos of rate of phase change.
Observe Galilean moons of Jupiter:
(4) Measure orbits of the four moons. I did this one in college with a Celestron 14. I believe the goal is to calculate the gravitational constant itself, which is a huge deal and watershed discovery for Kepler; but I've forgotten the details.