You start by getting your prequests done: http://royals.ms/forum/threads/zakum-prerequisite-guide.10723/ After gaining access to Zakum through doing the prequests, you'll have to attend a run and survive through till the end. To enter Zakum you need at least one Eye of Fire gained through completing the quests. All throughout the day, groups of Zakum hunters will smega for selling helmets and books. When this happens you'll PM them and tell them that you'd like to buy a helmet. They'll use mystic door to get you to Zakum's door from El Nath. I don't know what type of computer you're using but macs have a lot of trouble getting through zak normally. There are way around it though. During the fight, you'll want to change your graphics setting by one notch in either direction after all 8 arms are killed, and when the first and second bodies are killed to prevent graphical glitches causing you to disconnect. At the end, your name will be called to loot a helmet and then the group should tell you who to pay(Almost always in a FM store) Hug the left wall the entire time.
Zakum is a boss fight, first and foremost. Your party will be the ones kiling it and you'll be standing there in a corner hiding and doing your best to stay alive. You want to do what they call "hug the wall", which means constantly make sure you're right up against the left side of the wall. You dont want to get knocked into zakum's body and take touch damage- it deals anywhere from 6-9k depending on first , second or third body. Zakum helm sales are a trust between seller and buyer, as well. Some groups will have you pay up front and then take you on the run. If not enough helms drop, or for whatever reason you dont get one, they will refund you. Other groups prefer to have the person pay after they receive the helm, meeting up in the free market to pay. You need about 2.4k HP before HB to survive the unavoidable magic damage. If you're a mage, you just need magic guard and ginger ales/power elixers.