Can't believe I'm stuck already!

[square_is_the_best]

Well, I'm at the first Besaid Hotspot and I tried entering the cave at the ruins. It says its some kind of switch. I examined a few things that glittered every now and then. I examined number 8 and number 3 and I have no clue what it means. Help me please. And please no spoilers.

[Big D]

It helps if you talk to everyone in Besaid before you start that quest, like Lulu suggests. There are four "shiny things", each of which gives you a cypher - a number. All four cyphers are needed to unlock the machina gate at the entrance of the cave.

To find the four cyphers... talk to the locals.

[eternalshiva]

plus you need the search sphere for it, which you can only get from the chest in the temple and you need the Besaid Key, either you have 900,000 gil for it or wait until you rescue the people from Yojimbo's Fayth Cave in the Calm lands, on guy gives it to you.

[Big D]

You don't need the search sphere at first, that's only when you try to find the second set of cyphers.
The first four codes can be found just by examining the flashing lights located around the ruins and hills.

The second cyphers are an optional side-quest later in the game, so they're a little harder to obtain... but I believe that square_is_the_best is talking about the first cyphers.