I threaded wires through the top of the cage, around the hook of the hanging pot, up through the top again, then finished by wrapping the wires around each other tightly. It would help to have someone else hold the pot in position while you do this.
I've used 2 methods- but both require drilling a hole in the side of the pot that your plant is in... then either hang it with twist ties (dark black ones are my preferred) or fishing line. Just make sure any fishing line is tight to the screen, so that a stray tongue cant get cut.
All in all, twist ties are easier to hang hold strong.
what i did was take a pvc pipe ant put it at the top of the cage (could use wood or metal or whatever) and then i took some plastic coated floral wire and looped it through the screen then over the wire and that gave me a little loop i could hang from. the idea is to get the weight on the frame of the cage rather than the screen.
i should mention my planter came with a hook for hanging already so if you were curious about that and your planter didnt come with one you can try finding one pretty much anywhere they sell plants.