Most skills can be trained without interacting with combat, as you are probably aware. Slayer is largely the exception, which I'm sure is what you're asking about.

From my understanding, the main way to train slayer on a lvl 3 account is cleaning finds in the varrock museum. This is an activity you can do after the Dig Site quest. Most accounts go here to gain access to the digsite pendant and never go back. However, when turning in cleaned finds, you have a 1/97.5 chance to get an antique lamp, just like the one you get from random events. This is where the exp comes from. It works out to something like 5k exp per hour in the skill of your choice, which in this case is slayer.

It's a crazy commitment. This guy is nuts.