For battle, you will use actions from your action bar, which you can fill through the "Actions & Traits" menu. But as I assume you're rank 1 you'll automatically have your basic attack (whatever it happens to be) stuck on the "1" position. So the short version is to target the mob (tab or click with the mouse) and then press 1 (or press F to go into active mode and click the action by the 1), and keep pressing it every couple of seconds until the mob dies (or you do).
To try it out, go outside and look for a mob that has a blue circle to the left of its name when you target it (this means it's relatively easy). Go up to it, hit 1 and you'll automatically go into active mode (in this mode you can attack) and use your main attack action. You can hit 1 again whenever the stamina gauge (bar on the top) turns yellow, unless it's so low it doesn't fill up the thick part at the left of the gauge (that's how much stamina the action will cost).
As you play around with attacking you should get the hang of things so you'll be ready when you have more than one action available. And remember that there's no real penalty for dying, so don't worry if you end up getting eaten the first couple of times (but the marmots/rats just outside town are really really easy so should let you learn battle pretty quickly).
There's also the tutorial leve that you get as part of the intro quest. That'll have helpful tips on screen helping you through, but I can see getting to that point being a little confusing (you need to do the quest up until you get to the camp near your starting town, then the NPC will tell you that you have a guildleve, and you can do "Initiate guildleve" at the camp's aetheryte in order to start it).
FFXI: Triane [Caitsith], Retired DRK75, THF75, RDM71
FFXIV: Triane Rhiga
[Besaid] Pugilist, Marauder, Fisher