The infinitive form of a verb can be used several different ways without any conjugation.

As a noun - the subject or object of a sentence

• Mentir no es una buena idea.
  Lying is not a good idea.
• Aprender es importante.
  Learning is important.

After a conjugated verb, the infinitive can be used

A. With a preposition

• Vamos a estudiar.
  We're going to study.
• Acabo de salir.
  I just left.
• Salgamos depués de comer.
  Let's leave after eating.
• La biblioteca es perfecta para estudiar.
  The library is perfect for studying.

B. Without a preposition

Me gusta comer.
I like to eat.

No puedo dormir.
I can't sleep.

Teme bailar.
She fears to dance.

Creo estar cansada.
I believe I am tired.

Prefieren salir con nosotros.
They prefer to go out with us.

A los mexicanos les gusta ser amables.
Mexicans like to be friendly.

La tormenta amenazó destruir la casa.
The storm threatened to destroy the house.

Decidió nadar en el lago.
She decided to swim in the lake.

No logra estudiar en la noche.
He is not able to study at night.

Ellos quieren correr en las tardes.
They want to run in the afternoons.

Nunca aceptará comer carne.
He will never accept eating meat.

Acordamos darle un regalo.
We agreed to give him a gift.

C. With que

Tienes que comer.
You have to eat.

Hay mucho que hacer.
There's a lot to do.

In place of the subjunctive when the main clause has

A. the same subject as the subordinate clause

Tiene miedo que llegué tarde* ==> Tiene miedo de llegar tarde.
He's afraid of arriving late.

Estoy contenta que tenga razón* ==> Estoy contenta de tener razón.
I'm happy to be right.

*These are grammatically incorrect. When the subject is the same, you *must* use the infinitive.

B. an impersonal subject (if the subject is implied)

Es importante que trabajes ==> Es importante trabajar.
It's important to work.

No es necesario que vengan ==> No es necesario venir.
It's not necessary that they come (They don't need to come).