It's better for Midnight to explain, but basically we roll initiative and the DM rolls for enemy initiative. The turn order starts from highest score to lowest. There are exceptions to this order (eg. surprise rounds) but they need more specific explanations (and particular exceptions are often up to the DM to determine) which I don't think I'm qualified enough to answer.
Generally during your turn you can make -
One move action where you move your character,
One standard action eg. where you make an attack
One minor action eg. where you apply some sort of utility or bonus (or for some characters, an extra attack or lasting effect)
And others (like free actions which you can make as many as you like, I think?)
Generally in any order you wish.
There's a huge variety of what any of these actions can be, and there are lots and lots of exceptions to the rule (eg. Interrupts, Immediate) depending on player's characters. You don't
need to do all of them in your turn and there will be times where actions made during an encounter aren't necessarily on your sheet (like talking to an enemy, making a skill check which I believe requires a minor).
For example, I believe you can convert your move action into another minor action, and stored Action Points can grant an additional standard action in a turn.
But tl;dr the best way to learn how to battle is to do battle and let the DM explain stuff along the way, learning what constitutes standards, minors, moves, and what modifies them.
The new character builder sheet is particularly intuitive in this regard and calculates most modifiers for you - all you mostly have to do is roll dice, and learn how it is affected and how it affects other things on the board. Also, I haven't covered terms like At-Wills, Utilities and Dailies, because there's enough material here to wrap your head around for now, I think. =P
Btw do we have a grid or representation?
