How do I strengthen my feet for climbing?

Squats are a great overall leg exercise. The exercise really hits the major muscles in your legs that can help with climbing.

You don't even really need to add any weight to this exercise. Depending on your goals, if you just want to improve your leg strength for dynamic movements in climbing, even squatting with body weight can be enough.

If you want to go that extra mile, you can do a jump squat.
A jump squat is when you do a regular squat, but as you rise up, instead of just standing up, you jump as high as you can. This can help give you that extra strength training to get better at those dynamic climbing moves where you have to jump and reach a far away hold.

Other than squats, calf raises is another great exercise. All you need to do is to find a step or an edge to stand on with your toes, and you just raise yourself as high as you can while staying on your toes, and then you just lower yourself until your heel touches the ground. The higher the surface you are standing on, the lower you will have to go to touch the ground, which means it will be harder to complete the exercise.
If you feel that it gets too easy, you can hold a dumbbell or any other weight in one of your hands for extra difficulty.