For example, why is the "a" needed in "vamos a comer"? Why isn't it just "vamos comer"?
The periphrastic future is formed by "ir + a + infinitive", so "vamos comer" is not grammatical. You need to say: "Vamos a comer".
Most verbs that are followed by an infinitive will not take "a":
- Quiero comer (I want to eat).
- Prefiero comer (I prefer to eat).
- Deseo comer (I wish to eat).
- Pienso / Planeo comer (I intend/plan to eat).
- Decido comer (I decide to eat).
- Necesito comer (I need to eat).
- Prometo comer (I promise to eat).
- Intento comer (I try to eat).
Sometimes, "a" is used:
- Empiezo / Comienzo a comer (I begin/start eating/to eat).
- Me rehúso/resisto a comer (I refuse to eat).
- Vuelvo a comer (I eat again, I resume eating).
Sometimes, other prepositions like "de" or "en" are used:
- Termino de comer (I finish eating).
- Dejo de comer (I stop eating).
- Trato de comer (I try to eat).
- Pienso en comer (I think of eating).
Sometimes, "que" is used:
- Tengo que comer (I have to eat).
Therefore, the main verb (the one that precedes the infinitive) will define if any word will be inserted in between.
The preposition "a" will always be used if it precedes an infinitive of purpose:
- Vengo a comer (I come to eat = I come in order to eat).
- Salgo a comer (I go out to eat = I go out in order to eat).