Two of the major muscle groups in the ankle are the dorsiflexors and the plantarflexors. The dorsiflexors -- primarily your tibialis anterior -- raise the ankle in an upward direction and the plantar flexors -- primarily your calf muscles -- point the ankle in the downward direction. Both are important for normal gait, recreational sports and functional mobility.
To strengthen these muscles, you can do almost any activity that raises your ankle upward, although finding some resistance can help -- and resistance can include gravity. You could try sitting in a chair with your feet flat on the floor and raising your ankles and toes up, keeping only your heels on the floor. Another idea would be using ankle weights around your forefeet and dangling them off the edge of a bed and raising them up and back down. To begin, aim for a couple of sets to the point where your muscles fatigue and need a break.
For these muscles, you'll need to do exactly the opposite -- find an activity that works your ankles in the downward direction and that tires out your calf muscles. A tried-and-true method is heel raises, which are as simple as standing upright and raising up onto your toes and then back down. Another would be lying on your stomach with your knees bent to 90 degrees and moving your ankles up and down. If you have a resistance band you could straighten your leg, wrap the band around your forefoot, pull to create some resistance, and point your ankle downwards. There are many others, but as long as you feel the burn in your calves you're doing it right. Try the same routine -- do a couple of sets to wherever the muscles fatigue, then work up to more as you're able.