"A" precedes the following verb most of all in "perífrasis verbales". A lot of "perífrasis verbales" require an articlea preposition (a, de...) or some other conjunction (like que, in tengo que). Some examples are:
- Empezar/comenzar/iniciar/principiar a [verbo]: empiezo a comer
- Ir a [verbo]: voy a comer
- Ponerse a [verbo]: me pongo a comer
- Volver a [verbo]: vuelvo a comer
- Llegar a [verbo]: llego a comer
However, some don't. Some "perífrasis verbales" that don't require an "a" are:
- Deber [verbo]: debo comer
- Soler [verbo]: suelo comer
- Poder [verbo]: puedo comer
There are also certain "perífrasis verbales" that take the gerund form of the verb. Almost none of them require the "a":
- Estar [verbo]: estoy comiendo
- Seguir [verbo]: sigo comiendo
- Continuar [verbo]: continúo comiendo
- Llevar [verbo]: llevo comiendo [una hora]
"A" doesn't precede the following verb most of all when the verb can be replaced by a pronoun (i.e., when it's a subject or a direct object):
- Quiero comer — "comer" is a DO, and so it can be replaced by "eso": quiero eso
- Me gusta comer — "comer" is the subject, and so it can be replaced by "eso": me gusta eso
- Merezco comer — "comer" is a DO, and so it can be replaced by "eso": merezco eso
- Conviene comer — "comer" is the subject, so it can be reaplaced by "eso": conviene eso
Look how the replacement by "eso" doesn't work with the "perífrasis verbales" cited above:
- Empiezo a eso (wrong).
- Voy a eso (wrong).
- Me pongo a eso (wrong).
- Vuelvo a eso (wrong).
- Llego a eso (wrong).
- Debo eso (wrong).
- Suelo eso (wrong).
- Puedo eso (wrong).
- Estoy eso (wrong).
- Sigo eso (wrong).
- Continúo eso (wrong).
- Llevo eso (wrong).
Although some instances with "eso""eso/ello" instead of the verb in "perífrasis verbales" are idiomatic (such as "ponte a ello", "a eso vengo" or "ni a eso llego"), they are at least obscure from a grammatical point of view.
Bottom line: if you can susbstitute the verb by "eso", don't use "a". If you can't, use "a". If you do this, you will be right 3 out of 4 of the times. Three exceptions are "soler", "deber" and "poder", which don't require "a" even though you can't substitute the verb by "eso". Never use "a" before a gerund.