Could someone explain why sometimes there's something before and after the verb? I read the tips and notes but I still don't understand... Also could you give me a list of them (so I can take a note of them :))
First of all, there are stressed forms and unstressed forms. The unstressed forms are placed before the verb and are mandatory, even if you also choose to add the stressed forms.
He gives me a book = El îmi dă o carte.
He gives you a book = El îți dă o carte.
He gives him (her) a book = El îi dă o carte.
He gives us a book = El ne dă o carte.
He gives y'all a book = El vă dă o carte.
He gives them a book = El le dă o carte.
These forms might change if the verb is in some tense other than the present (to mi, ți, i, ne, vă, le - followed or preceded by a dash that indicates they are to be pronounced together with whatever comes before or after the dash):
El mi-a dat o carte = He gave me a book.
Vreau să-mi dea o carte = I want him to give me a book.
If you want to place extra emphasis on the dative pronoun (i.e., He gives a book to me), you can also place the stressed form after the verb, but the unstressed form must also stay before it, otherwise it's incorrect:
El îmi dă mie o carte = He gives me a book.
The stressed forms are: mie, ție, lui/ei, nouă, vouă, lor.
You can also shift the stressed forms around the sentence in order to shift the emphasis, word order is quite flexible in Romanian, though the standard and more neutral way to say it is just after the verb.
Mie îmi dă o carte. Îmi dă o carte mie. [the meaning of these sentences might depend a bit on the intonation, but it tends to be something like 'It is me he is giving a book to']
I hope this helps!