This extends to more than just planets, too. The University of Maryland Observatory runs a summer program for amateur astronomers that I signed up for this year, and we're learning how to do exoplanet transit detection. There are databases to look up candidates and ways to submit data to reinforce findings. It's doable with typical telescopes available to amateurs, and the observatory has a few larger scopes we're learning to use. One of the professors at UMD has written up guides on how to do it: http://www.astrodennis.com/

Other efforts like this include: - American Association of Variable Star Observers https://www.aavso.org/public - Center for Backyard Astrophysics http://cbastro.org/

and I'm sure there are others I don't know about.