Also Adeline, keep your upper body in mind. Sit up and don't lean but simply look where you're wanting to go. Your shoulder will turn slightly and this also affects your hips causing you so apply more inside leg to keep your horse from cutting the corner. If they are really bad about it you can always practice some counter bend in both directions to improve balance.
Place four cones in a square shape and ride a circle in it as much as you can.
Give the horse responsibility. Put him in the circle and correct him if he deviates. The first full circle he does which is improvement, turn him to the middle of the circles and give him a break and then repeat. He will understand that a good circle means break and will try to achieve that.
Expect a lot, accept a little, reward often.
Hi Adeline, additionnaly to the previous advices, make sure that you don't always turn at the same places of the arena or don't ask the same exercices in the same order so that the horse does not anticipate. Every time that you make a figure (circle, diagonal etc...) you should also make your horse wait as much as possible before turning to teach him patience and precision :)
An equal length on the reins and keeping your inside leg on a bit helps! Sometimes I think like I'm spiraling out and then my horse doesn't try to cut circles!
Make sure your reins are equal in length, and that you have a good contact, i.e that you can feel his mouth resistance, but not enough so he thinks you're asking him to stop. Outside rein stays still, and inside rein can be tweaked, rather than pulled to the side (instructors teach this because it's easier for the beginner rider to do, but you will be later taught do do a smaller/similar action) so, if you have the correct contact, all that will be needed is to point your knuckle forwards, this will tweak the rein enough on his mouth and together with the inside leg coming slightly behind the girth, horse should turn left/right without any problems ! The problem comes from the horse wanting to turn earlier than the rider wants :)
Your outside leg (one nearest the wall) needs to stay on the girth - to keep the forwards movement, your inside leg (one nearest the centre of the school) can come back slightly to ask for the bend needed.