They can be either direct or indirect.

Pronomi diretti:

mi = me
ti = you
lo = him
la = her
ci = us
vi = you
li = them
le = them ("li" female version)

Some examples:

Li ho visti = I saw them
Non la conosco = I don-t know her

If there are either 2 verbs in the same sentence or a gerund or imperative direct pronouns are after verbs and "merged together":

Examples:

Vengo a trovarti = I come to visit you
Penso di conoscerla = I think I know her.

Note: Ecco + direct prononuns = eccomi/eccoti,eccolo,eccola,eccoci, eccovi, eccoli, eccole (here I am, there you are, here he is, here she is, here we are, there you are, here they are).

Pronomi indiretti

mi (a me), ti (a te), ci (a noi), vi (a voi), gli (a lui/a loro), le (a lei)

The only differences between direct and indirect pronouns are gli and le.

The indirect pronouns are used when we address the speech to a thing or a person. They follow the same rules for direct pronouns.

Let's see some examples with "gli" and "le" :

Spiegagli l'esercizio = Explain them/him the exercise.
Spiegale l'esercizio = Explain her the exercise.

I know, it seems to understand when I should use either li or gli, either la or le.

When you have this doubt, ask yourself the following question:

Is the action address TO what/who? If your answer is YES, use indirect pronouns. You should add an "imaginary to/for" before the indirect pronouns. It should help.

FARE/ANDARE
Fare and Andare can be used with different meanings if they are added to an indirect pronoun:

Mi faccio prendere un caffè = I gonna ask for a coffee.

Here FARE + INFINITO is a spoken Italian sentence.

Non gli va di uscire = He does not want to go out.

Here ANDARE means "wish" , have a willing to" and it ony has two forms: va (singular) and vanno (plural).