This page discusses the various actions that heroes can take. In Heroes of Gaia, all actions that don't concern building/research are hero actions. You can't send troops around without heroes.
Action Points
Any action your hero takes requires action points (AP). The total number of action points is based on your level (and hence fame). Once spent, you automatically regenerate 10% of your total action points per hour, whether you are connected or not. Keep an eye on your action point total (bottom right of map window, if you can't see it click on that light-colored square at the bottom - or the Player tab in a castle).
Tip: If you're going to be offline for 10 hours or more, try to use up as many AP as possible. If your AP is at maximum you don't gain any more.
Every day there is a period called Happy Hour. This is two hours during which most AP costs are halved. Costs for visiting World Map buildings aren't halved, but everything else is. This is especially useful if you're planning on attacking a player since this costs alot. It also means that this is the time you are most likely to be attacked, so take care. Happy hour starts around 4am GMT but since server time seems to shift in relation to real time this does vary somewhat. It always starts at 20:00:00 server time.
Tip: Make sure you have alot of AP just before the happy hour if you're planning to make use of it. There's little worse than running out of AP near the start.
Attacking NPCs
There are a number of NPCs scattered around the world map. Your hero can attack any group you choose. Daily quests reward you for doing this, based on your level. You also get a small amount of a random resource and some gold from this.
Attacking Items
There are also items scattered around the map. Your hero can attack the NPCs guarding the treasure, allowing you to add the treasure to your empire. This means that you can equip the new item to any heroes that have high enough level.
Attacking Resources
Resources are also scattered around the map. These vary from one-star to five-star and while all are guarded by NPCs the defense forces are extremely weak. Hence this is a good starting point for newbies. It costs 6 AP to attack a resource, or 3 AP during happy hour.
World Map Buildings
A number of free-standing buildings are scattered around Gaia. Visiting them can bring rich rewards.
Attacking Players
Heroes of Gaia is a war game, so eventually you will attack other players. PvP is the biggest challenge and can bring great rewards. Its AP cost is very high though.
Conquest
One of the first things a new player wants to do is conquer some mines to increase their production. Once more experienced, it is good to conquer castles and perhaps even help to conquer a capitol.