1. Flag control. The more flags you control, the faster your warscore rate goes up.
2. Generally people get 2 helms and 3 health items. Some opt for 3 helms for mana intensive characters (queen of thorns, rook, oak) while others opt for 1 for less mana intensive characters (beast, torch bearer). But usually 2. Unbreakable boots are a must for pretty much everyone.
3. Unclean Beast, Oak, Erebus are all very noob friendly. I would suggest picking one and sticking to it until you feel confident with that demigod.
4. You can teleport with scrolls (250g each). There are favor items that increase movement speed or act as teleport scroll. There are items you can buy to increase your speed by 10-20%, and these stack. One item has an on use ability to increase your speed by 50% for 8 seconds, another item has a % chance to increase your speed greatly.
5. Experience. Also, looking @ strategy guides posted for characters will give you a layout for which items to buy, what build to go, etc.
6. Check out the strategy section for an extensive list Conveniently Nucleus Accumbens listed all the best posts into one nice post here: http://forums.demigodthegame.com/365172
gl and hf! Just make sure that when / if you go online to join or host noob games at first to test the waters and gain playing experience