Wakka is probably Tidus' best friend in Spira. Sparked by a shared interest in Blitzball, the two connect right away. Eventually they become more like close brothers than friends.
When Tidus washed up in Besaid after being separated from the Al Bhed during an attack by Sin, Wakka and his Blitzball team, the Aurochs, were the first people Tidus met. Floating alone in the water, Tidus was unexpectedly hit in the head with a Blitzball. Tidus was so happy to see the Blitzball because it was something from his world in Zanarkand. He hit the ball back toward the shore using a fancy technique I'm sure he picked up playing professionally. Wakka and his Aurochs were awed by Tidus' skills and wanted to see more.
The Aurochs were a pretty terrible team. Tidus being a star on his old team, the Zanarkand Abes, probably would have impressed Wakka and the Aurochs with any move he showed them. Wakka recognized his skill right away and asked what team he played for. When Tidus answered, "the Zanarkand Abes," and then lied and said that he was affected by Sin's toxin, Wakka took Tidus under his wing.
Wakka definitely had his own motives by being kind to Tidus. He wanted Tidus to play for the Aurochs so that they would have a chance to win. I think Wakka would have done right by Tidus regardless, though. Wakka has a huge heart. Furthermore, Tidus reminds Wakka a lot of his deceased brother, Chappu.
Chappu used to play Blitzball, but gave it up and became a Crusader. He was killed while battling Sin. Something hugely important about Chappu is that Wakka had given him a sword called the Brotherhood to fight Sin with. When Chappu went to fight Sin, though, he chose to leave the sword at home and used Al Bhed machina instead. (I think that's a big part of the reason Wakka doesn't like the Al Bhed.) Wakka gave the sword Chappu left behind to Tidus. I think that symbolized how Wakka felt about Tidus. The sword was called the Brotherhood, after all.
Throughout the game, Wakka and Tidus poked fun of each other like brothers typically do, and Wakka watched out for Tidus like an older brother would. Wakka wanted the best for Tidus, and took a lot of crap from Lulu for trying to help him out. Wakka never made a decision for Tidus, though, and even insisted to Lulu that being a guardian should be Tidus' decision when Lulu persuaded him to ask. Tidus agreed to become a guardian, of course, and I think Tidus accepted the position not only because he wanted to be around Yuna, but because he wanted to be around Wakka.
Strain was put on their relationship when Rikku joined the party. Tidus was put in an awkward situation because he knew that Rikku was an Al Bhed, and he knew how much Wakka hated the Al Bhed. He kept the truth about Rikku from Wakka so that Wakka wouldn't be against Rikku. Wakka got mad at Tidus and Lulu for hiding Rikku's heritage from him, but he got over it quickly. Tidus and Lulu even helped him learn to see Rikku as a person rather than as her race.
There's no way that Wakka could stay mad at Tidus for long. Along with Yuna and Lulu, Tidus was very much like family to Wakka. Both of them had lost family to Sin, and in their time of need, they were able to be what each other needed. It seems what they both needed was a brother.