Trills are often the hardest thing for young pianists to master. Most of the issues come from playing them too fast, from playing them with too much tension, and with too much finger movement. The good news is playing them slower, with a relaxed hand, and with as little movement as possible makes them way easier!
First of all never play trills faster than you can move your fingers. I know that’s obvious, but I hear people try this all the time, and it sounds terrible! Start out by playing the two notes of the trill extremely slowly. Never let your fingers leave the keys. Gently depress the key, when its time to play the next notes gently raise the key, but do not lift your finger from the key. Slowly increase speed but stop accelerating before any tension comes into your hand or arm or upper body. Try making this a daily exercise and you will be able to play trills at any speed in no time.
Remember that you can use any fingers for trills. 1/2 and 2/3 are very common. But also try combinations like 1/4. Once you use combinations with fingers further apart such as 1/4 you can hold your fingers more still and engage your wrist to play the trill. Try playing the same trill with 1/2, 2/3, and 1/3, 1/4 and see what the difference in sound and mood is. Don’t forget to practice trills with both your right hand and your left hand.