Probably the best option available to free players is item flipping on the Grand Exchange. It’s basic economics— buy low, sell high. First, choose an item to flip. Medium-level runes like law or cosmic tend to work well, as well as steel bars or mithril ore.
Buy a small amount of the item just below the market price and sell it just above to see how much profit you can make per transaction. 5 gp per flip is good for runes, and 20 gp per flip is a good rate for metals. Once you’ve found a good item to flip, buy and sell it in bulk in order to make a large profit. As you get more money, you’ll be able to make a larger and larger profit.
While you wait for flipping transactions to complete, there are a few other things you can do to supplement your profits in and around the Grand Exchange. If you have a woodcutting level of 60 or higher, you can cut yew logs behind the palace.
Another source of both xp and money is killing guards, who occasionally drop valuable grapes. Fletching headless arrows, making pastry dough from flour, and collecting ashes are also good sources of income.
Using all these methods, you should have the six million gp required for membership within a week or two of casual play. Buy your membership bond and enjoy the world that opens up.