0) The indirect pronoun always goes before the direct pronoun;

0) The indirect pronouns mi, ti, ci, vi followed by the direct pronouns lo, la, li, le become me, te, ce, ve;

0) The indirect pronouns gli and le followed by the direct pronouns lo, la, li, le join together by means of an “e” and form one single word: glielo, gliela, glieli, gliele (these are valid for both men and women: even “le” becomes “gli”).

Ok, now you have the three rules you needed. How should the previous sentence be transformed, then?

Luca scrive a Claudia una lettera

With this sentence we need rules #0 and #0:

Luca gliela scrive (Luca writes it to her)

It’s easy, isn’t it? But let’s make other examples!

Giulia dà a me un regalo [rules #0 and #0] → Giulia me lo dà (Giulia gives me a present → Giulia gives it to me)

Paola compra un computer al suo ragazzo [rules #0 and #0] → Paola glielo compra (Paola buys a computer for her boyfriend → Paola buys it for him)

I miei genitori hanno prestato un libro a me e mio fratello [rules #0 and #0] → I miei genitori ce lo hanno prestato (My parents lent me and my brother a book → My parents lent it to us)

Now, there’s only one last question to discuss… What happens with the pronoun of third person plural “loro“?

Federico regala a loro i suoi gioielli (Federico gives his jewels to them)