Chapter 1: Game Basics
Walk around with the left analog stick, unless you are old-school and you like the directional pad. Using the analog stick affords you more options, though. Pushing the stick further and further in one direction makes your character walk faster, then jog, then run. Holding the R2 button will put you in walk-only mode, which is useful for sneaking around enemies. Coming into contact with an enemy will put you into a battle.
The circle button
Hit circle to open doors, talk to people, open boxes, take items, hit big red switches, read maps, activate cranes, or do pretty much anything else that involves interaction with the environment around your character.
The big rotating yellow things are save points, and you can save your game at them by hitting O. You may also recover your characters' stats at one by using a Bio Sphere. If the save point has a blue plate attached to the top of it, then it has few additional features: you can play Xenocard, play AGWS battling, visit the casino, or use the E.V.S.
The big rotating silver things are shops. You can buy or sell items and equipment there.
Blowing stuff up
You can use the U.M.N. to blow stuff up. If your character passes by an object that can be blown up, a blue indicator will appear and a sound will play. Hit square to blow that object up. You may open up new areas, discover items, or encounter enemies when blowing stuff up. Some stuff, when blown up, will release some kind of temporary ill effect for your enemies on the field (lightning, fire, etc.). If you can lure an enemy into one of these, then the effect will be displayed. If you then fight the enemy, it will be at an appropriate disadvantage.
In the lower right corner, there is a blue radar screen. Your character's location and facing are indicated by a red triangle. Enemies are indicated by yellow triangles. Non-hostile characters are indicated by green triangles.