(GE=Grand Exchange)
Well, there is a few (good) ways to make money for the f2p people:
Spawns
Red spider's egg: found under Varrock in the sewers, 2 spawns. When you are close to the eggs or got some in your inventory the spiders level 34 will attack you all at once if you're not standing in a corner. Sell the eggs in GE for 260-398gp each.
Fishing
Lobsters: fished at Karamja. Take the boat from port Sarim. Bring money for boat ride there and back. Sell them in GE for 201-212gp each.
Mine
Silver ore: mine it at the Crafting guild (best place). There is also some outside champion's guild. Sell them in GE for 162-180gp each.
Gold ore: mine it at the crafting guild (best place) you can also find them in the Falador mines (2 stones). Sell them in GE for 491-543gp each.
Coal: mine it under Falador (5 stones) and store it in the Falador bank. There is a pair north in Al Kharid. You can also mine in the Mining guild if you got level 60 mining (37 stones) sell them in GE for 154-172gp each.
Woodcutting
You can ether cut willow or yew (depending on your WC level). Willow outside Draynor village bank or at port Sarim (at east)
Killing beasts
Big bones: kill giants ether down the Varrok sewers, down the Edgeville Dungeon or at Cranor isle Sell them for 378-418gp each.
Cow hide: kill cows outside Faladow, Al Kharid or outside crafting guild, take the hides and store them in the bank. When you got enough sell them at GE for 112-124gp each.
Wizard robe: found when killing level 9 wizards at wizard tower. Bring some food (depending on your lvl) because the wizard will hit and damage you, like 4-5. My level 63 needed 5 to make a good amount of robes. Sell them in GE 708-784gp each.
You also get wizard hat, BUT do not sell them at the Grand exchange, you only get 1-2gp for them.
And of course you get runes like chaos, law and nature that you can sell at GE for some money.