Weapons
Equip weapons in your inventory (default key: tab or backspace), by pressing use (default key: left control) and up. Usually it will put a sword/axe/mace in hotkey slot 1. Press 1 to access it for battle or your fight key (selects last used weapon).
Bows and Crossbows usually go into slot 2. They require ammunition to fire. (bolts for crossbows, arrows for bows) Bows and crossbows do not require the ammunition to be equipped and are used automatically if you have them.
Armours
Armour is equipped the same as weapons. You can get your first sets from either Fisk in the old camp or the templar at the gate to the sect camp. There should be a set for the new camp, but I haven't seen it yet.
As you join a new guild and gain influence more armour will become available. Your first set will cost around 500 ore.
Food
Use food just how you would equip a weapon to restore health or mana. Be sure to cook any raw meat in the pans in the camps to increase their qualities. There is also a cheat with the raw meat, so you may not want to cook it all.
Special equipment
Special equipment such as rings and amulets can be equipped to give bonuses to your stats (eg: +10 hp).
Magic
Magic is equipped same as weapons and uses slots 4 and onwards. NPCs also recognise most magics as a weapon and will try to attack you if you walk around with it in cast mode too close to them. Spells like sleep however are fine.
Scrolls are 1-shot weapons, but stones have unlimited use. Get your first stones from the water mage in the middle of the new camp for 500 ore.
Misc.
Most quest items go here and are unusable or just there for trading.