The preposition is an invariable part of the sentence that establishes a relation between two words. They don't have a meaning of their own and show position, time, relationship, etc. between words. Let's look at sentences which follow the formula conjugated verb + preposition + infinitive

Some verbs are followed by the preposition "a" and then the infinitive form of another verb. We can write a formula for this construction as: conjugated verb + preposition "a" + infinitive

A few examples of verbs which use the formula above are: aprender a, ayudar a, enseñar a, comenzar a, correr a, ir a, invitar a, negar a, principiar a, salir a, venir a, volver a

Él corre a jugar.

verb = correr (present indicative)
verb = jugar (infinitive)

Tú corres a trabajar.

verb = correr (present indicative)
verb = trabajar (infinitive)

Ellos salen a caminar.

verb = salir (present indicative)
verb = caminar (infinitive)

Tú vienes a oír.

verb = vienir (present indicative)
verb = oír (infinitive)

El niño comienza a caminar.

verb = comienzar (present indicative)
verb = caminar (infinitive)

voy a escribir.

verb = ir (present indicative)
verb = escribir (infinitive)

Other verbs are followed by the preposition "de" and then the infinitive form of another verb. We can write a formula for this construction as: conjugated verb + preposition "de" + infinitive

A few examples of verbs which use the formula above are: terminar de, tratar de, dejar de, terminar de, parar de, dejar de, olvidar de

Él termina de comer.

verb = terminar (present indicative)
verb = comer (infinitive)

Tú tratas de trabajar.

verb = tratar (present indicative)
verb = trabajar (infinitive)

Ella deja de jugar.

verb = dejar (present indicative)
verb = jugar (infinitive)

Another group of verbs are followed by the preposition "en" and then the infinitive form of another verb. We can write a formula for this construction as: conjugated verb + preposition "en" + infinitive

A few examples of these verbs are: consentir en, insistir en, tardar en

Él insiste en salir.

verb = insistir (present indicative)
verb = salir (infinitive)

Él tarda en llegar.

verb = tardar (present indicative)
verb = llegar (infinitive)

Ella esta consiente en trabajar.

verb = consetir (present indicative)
verb = trabajar (infinitive)

Nota:
El verbo que no va en forma infinitiva y que necesita alguna de las preposiciones mencionadas, antes de seguir con otro verbo en forma infinitiva, puede estar en tiempo: pasado, presente y futuro.