When do I use the subjunctive instead of or in place of the infinitive?

Do I need to use the subjunctive after Poder+verb? For example: El sistema le puede ayudar valora... Or do I need to use the infinitive? El sistema le puede ayudar valorar...

In the above mentioned example, you need to use the infinitive (el sistema le puede ayudar valorar) because there is no subject change.

To know if the infinitive may be used in place of the subjunctive, ask yourself the following questions:

1. Are the subjects of the subordinate and main clause the same? For example, compare the following:

Yo quiero ir.	I want to go. (no subject change)
Quiero que ella vaya.	I want her to go. (subject change from I to her).

Generally, when there is no subject change, the infinitive is used.

2. Is it an impersonal construction? See below

Hacía falta agregar azucar.	It was necessary to add sugar.
Se evitaba hablar de su esposa muerta.	People avoided talking about his dead wife.

3. Is the verb followed by the preposition 'a'? With certain verbs, even when they are not impersonal and have different subjects, the infinitive may be used.

animar a	to encourage to	te animo a continuar / que continuen...
forzar a	to force to	él quiere forzarlas a ver / que vean...
impulsar a	to impel to	impulsar a los gobiernos de todo el mundo a destinar / que destinen más dinero...
incitar a	to encourage to	Incitar a hacer click / que hagan click

4. Does it use any of the following verbs? The following verbs may use subjunctive or infinitive, but are not followed by 'a.' When they use the subjunctive, they must be followed by que:

dejar	to allow / let No me dejaron salir que saliera. (The wouldn't let me out.)
mandar	to order Les mandé limpiar / que limpiara la cocina. (I ordered them to clean the kitchen.)
pedir	to ask (request) Te pedí callarse que te calles. (I asked you to be quiet.)
permitir	to allow / to permit No me permitió comerse /que se comiera las uñas. (He wouldn´t allow me to chew my fingernails.)
hacer	only when it means to make someone do something or feel something: Le hice sentirse / que se sintiera mal. (I made him feel bad.)

Other verbs that follow the above rule:

impedir	to prevent	prohibir	to prohibit
sugerir	to suggest	obstaculizar	to hinder
ordenar	to order	recomendar	to recommend