The verb WANT is followed by infinitive with TO

I want to go to Rome
She wants to learn Spanish
Everybody wants to win

But when we have two different persons involved, we use this construction:

subject + Want + object + infinitive with to

I want to go I want + I go (I = I)
I want him to go I want + he goes (I / he)

They want us to do the job
She wants me to stay with her
I want you to come with me
He wants them to repair his house in two months
I want David to work with me  (not: I want that David works with me)

Negative and interrogative form

(+) I want you to come with me
(-) I don't want you to come with me
(?) Do you want me to help you?

For more advanced learners

Two different negatives. Compare:

They don't want + I do it = They don't want me to do it  (absense of will)
They want + I don't do it = They want me not to do it  (negative will)

I don't want you to go, I want you to stay with me
Stop, stop! I want you not to touch anything until I give the order

A few other verbs use this same construction: would like, ask, expect, help, mean, allow, need, order...

I expect them to finish soon
I'd like you to come with me
She said she would prefer us to visit her tomorrow
He asked me to hurry up
I didn't mean her to cry
They helped us (to) put the sofa inside the house
They don't allow people to smoke here
I need you to wait for me