You can do body weight exercises. You can also invest in some dumbbells or resistance bands.
Self.com has a lot of various things you can do that don't involve weights
You can also do a search online for body weight exercises or resistance band exercises.
Pushups, squats, lunges, plie squats, tricep dips, etc all don't require weights other than your own.
I've started doing kettlebells which only requires one piece of equipment. I found mine at Target.