believe > to believe ( suject BE to-inf)
All you have to is to fit the pieces together.
The thing to do is to pretend you didn't hear.
His greatest pleasure is to sit in the pub talking to his friends.

Me suena la frase como:
Solo tienes que confiar en mi.

Pero no he encontrado ninguna definicion de belive como confiar, solo como creer.

@wallebot: Tienes razón. "to believe someone" quiere decir creer lo que ha dicho alguien, o confiar en alguien.

I don't know your language. No translation mistake but structural one. I cannot understand what you mean.

@duran: wallebot had a different concern. As for yours, the "to" is optional in some cases. (In the examples you gave, you could omit it from the first two, but not the last. Why? I don't know.)

Spoken English and Grammatical written English is very different. You can omit, add or change a lot of things in spoken English. In fact, you can omit "to's" from all sentences above in spoken English, but not in written one. Some other examples:
I wanna go with you.
I gonna finish it tomorrow.
I am not= I ain't
I want 2 go
U wanna drink something? etc.

No, this is not colloquial. You can omit the "to" even in standard written English.