After some of the introductory scenes, you’ll regain control of the main character on what I’ve always assumed to be some kind of boat, though it’s never been easy to tell. In any case, speak with mostly everyone around here to get some conversation done and a superficial background on the character you’re controlling, who you also will get to name (probably Tidus, to make it easy on everyone involved unless you prefer Meg Ryan). Afterwards, you’ll end up on a highway overpass. Run along it for a while; as you go along, speak with everyone on the way - one (a girl in a pink shirt) should yield you two Potions , so long as you tell her you have some spare tickets. Which you probably don’t, but there are bigger problems to come, regardless. Eventually, you’ll be allowed to proceed into the blitzball stadium at the end.
Enjoy the awesome blitzball sequence there before things get really … uh … whoa.