Are there rules of verb conjugation?

See a translation

By "the rule", do you mean the participe passé (the -er verbs turn into avoir ou être + -é) ?
The other are indeed irregular. Actually, there are 3 groups:

• The 1st contains all the -er verbs. When you use the participe passé, they become avoir or être and end in -é. For example, with "manger": "Je mange" (present) becomes "j'ai mangÉ" (avoir + manger) with the participe passé.

• The second one is complicated: it is about the -ir verbs, but not all of them.
The verb "finir" (= to end) is one of them. If you use the participe passé it turns into être or avoir + -i. ("J'ai fini" = avoir + finir).

• The third and last group is all of the others verbs.

I know, this is reaaaally boring and complicated and there is no logic at all ^^' Conjugation is one of the main things that make Franch such a difficult language to learn when you are not native.
You have no other choice but to practice again and again, by reading and listening french.

If you have other questions and if you are not afraid of my sh*tty explanations, I can still help you though, so feel free to ask :)

I hope it helped you a bit :)