Instructions
Become an official member of RuneScape. While non-members will experience some random events, other random events are exclusive to members only -- meaning if you're a member, you'll see more random events.
Chop wood, preferably Yew trees, as they offer the best profit margin. The longer you chop wood, the more likely you are to encounter a random event.
Don't enter any form of combat training. RuneScape will not teleport you into a random event if you're engaged in any form of combat.
Avoid completing any events. According to RuneScape.com, "Random events will occur with a certain degree of regularity, but if you consistently complete events successfully, you will encounter them less frequently."
Go fishing. As fishing doesn't count as an event, you can improve your fishing skill and make money while waiting for a random event to occur.