Some general considerations:

Federer speaks colloquial British English and Nadal speaks colloquial English with a Spanish accent and a few mistakes. As they are speaking informally and laughing a lot, their sentences are often broken, uncomplete and mixed. Pronunciation is often obscure or down to a mumble. Self-corrections and second thoughts are frequent. All that happens a lot in informal conversations. It is also common the overuse of the preposition LIKE, even when it means nothing.

The future form they're using is GONNA, which can be used with or without the verb To Be:
- You gonna play = You're gonna play = You're going to play.

A FIT OF LAUGHTER= When you start laughing and you can't control it.

GONNA= (informal) Going to.

I TELL YOU= When talking, we can use this phrase at the end of a sentence to emphasize what we just said: - Oh man, this is too big, I tell you.

PROMOTE= To promote a product is to advertise it so people know about it and/or buy it.

MATCH= Tennis match (a game of tennis).

SHALL WE...?= A common construction used to make a proposal:
- Shall we go to the cinema? = Why don't we go to the cinema? = How about going to the cinema? = Let's go to the cinema!

THERE WE GO!= An expression used to announce we're going to do something planned or expected.

YET?= This YET goes with the verb KNOW, so the sentence means "do you know it yet? Or maybe you are still undecided?"

YOU KNOW WHAT?= We can say this before a sentence when we want that sentence to sound more interesting (we are generating curiosity in advance), and it's not a real question.
- You know what? I'm really hungry.

AN EXHIBITION MATCH= A match which is not generating points for competition, it's simply a friendly match, the result is not official.

FOUNDATION= /faʊndeɪʃən/(Rafa mispronounces it) An institution created for a purpose, usually for charity or to help a certain group of people.

HERE WE GO!= Exactly the same as THERE WE GO! (see above).

WHAT YOU GONNA GIVE ME= (coll.) What are you going to give me.

GET ME= Give me.

HOW 'BOUT = HOW ABOUT= One of the common ways of expressing a suggestion (see above):
- How about going to the cinema? = Let's go to the cinema!

I COME PLAY= (coll. esp. AmE) The standard form should be "I come to play" and we would say "How about if I come to play an exhibition...?".
Standard: - I'll come/go to play
Colloquial: - I'll come/go and play
Very informal: - I'll come/go play

COOL= (coll.) Fantastic, wonderful.

¿QUÉ DICE, QUE ESTABA MAL? ¿ESTABA MAL O QUÉ?= Translation from Spanish: What did he say? He said it's wrong? Was it wrong or what?
Federer is simply laughing for no reason, he just can't help it, but Nadal feels that maybe Federer is laughing because he is using bad English. This situation is very common, when a student feels insecure about his level of English, if people laugh he thinks maybe they're laughing at him, but natives very rarely laugh at foreigners' mistakes (unless they happen to say by mistake something which sounds really funny in English).

GEES!= A mild exclamation of surprise, admiration, etc (euphemism for "Jesus"). This exclamation is mainly used in AmE and it is more common to say simply GEE!

LAUGH= The standard British pronunciation is /lɑ:f/ but many people say /læf/, which is also the standard form in AmE.

NO PUEDE EMPEZAR, TÍO. ES IMPOSIBLE QUE LO DIGA YA= Translation from Spanish: He can't start, man. Now it is impossible for him to say it.

ESTOY SUDANDO COMO UNA BESTIA, TÍO= Translation from Spanish: I'm sweating like a pig, man.

I GUESS...= (coll.) I suppose…

I'D RATHER + infinitive without to= I prefer + infinitive with to:
- I'd rather stay here= I prefer to stay here.

FELLOWS (coll. BrE) = GUYS (coll. AmE) An informal way of addressing other people: - hi fellows, how are you doing?

SET= Each part of a tennis match is called a set. "I'll give you the first set" means "I'll let you win the first part of the game".

HOW'S THAT?= (coll.) What do you think about it? Do you like the idea?

ZURICH= The capital of Switzerland. Nadal pronounces this word with a Spanish accent from Spain /θurik/, but the English pronunciation is /zjʊərɪk/
o también (esp. AmE) /zu:rɪk/.