When two pronouns meet
You know the object pronouns one at a time: Je le vois, Je lui parle. When you replace both objects in a sentence, the pronouns stand together where a single pronoun would stand, and their order is fixed. English can say I give it to him or I give him the book; French has no such choice.
The two commonest combinations
Two patterns turn up most often, and they are mirror images of each other.
Person first or thing first?
me / te / nous / vous + le / la / les
If the recipient is I, you, we or you (plural), the person comes before the thing.
Tu me la prêtes, ta voiture ?
Your car: will you lend it to me?
Je vous les envoie ce soir.
I'm sending them to you this evening.
le / la / les + lui / leur
If the recipient is he, she or they, the thing comes before the person.
Je le lui rends demain.
I'll give it back to him tomorrow.
Nous les leur avons montrés.
We showed them to them.
English always puts the thing first: give it to me, give it to him. French does the same only in the third person (il le lui donne) and flips for I/you/we/you (plural): il me le donne.
y and en at the end
y and en come last, after all other pronouns. Before them me, te, se, le, la become m', t', s', l'. y and en together occur practically only in il y en a.
Des places libres ? Il y en a encore deux.
Any free seats? There are still two.
Ce problème ? Je lui en ai déjà parlé.
That problem? I've already talked to her about it.
Tu m'y emmènes en voiture ?
Will you drive me there?
Du gâteau ? Elle nous en a apporté.
Cake? She brought us some.