well these are the top three ways i think a F2P can make money. I
personally like Rc'ing at the moment but it is also the slowest to lvl up.
Mining i consider the most consistant but you have to be at ur desktop the
hole time. Yews are great if u want to do many things at once. Just find
a spot where not many people go, Rimmington/NorthEast of Varrok or
any other spot u can find. This is great eairly on but once u get up higher
in the lvl's the others pay off tons more. The mining gets up to the most
amount once your smithing/mining lvl are high. Now to Rc. For f2p i like
to craft airs. You can find buyers for 20ea and it is a really short walk. I
do this when i got many friends on and i just talk to them the hole time
really. It also adds up to becomming quite a bit at a high lvl. And if u are
ever thinking about becomming a member i think this is the way to go. It
is really great when you get loads of them at once. A example is this
week ive crafted about 50k or so Airs and earned over 1mil. All i did was
talk the time, yes it was quite a while but i lvl'ed up 7 lvls and got a good
payment. So pick one of these ways that best suits ya and try it out
once.

i do a mix of all three and they all work great for me money
wise
EDIT- ok now i have a little more time so i can go into details about it.
WC/Woodcutting- Good places to chop vary around location/distance to bank/how many other users chop there. I've recently been looking for places to find yews without other choppers to increase the amount that i chop.
reg. trees -chop anywhere
Oaks- I thought a good place was in lumby right behind their shop. You can chop untill your full then just sell at the store. Oaks arent enough to sell around at banks yet.
Willows- Chop right around Drynor bank- many other choppers will be there but the tree's respond fast enough- this is where u first start making a good profit on logs. A lot of people trying to get firemaking lvl up will buy these log. They sell between 15-30 ea depends on how many and who it is your selling to. This place to cut is right, and i mean right, beside the bank. easy storage. It's better to start selling loads at a time now also. Store 1-5k logs then sell them.
Yews- This one is mainly up to you. South of Fally/falador has three trees, but many people cut there. The more people cutting the less profit you get. Edgeville has 2 yews right beside a bank. Load of talking there so if you arnet worried about losing some time and yews then go here. A lot more higher lvl Wc'er go here. Now, i havn't tried this but my friend has informed me that Rimmington is a good place to go for yews. Yes, it is far from a bank but it has 5 yews and very, very few people go here to cut. One of my favorites, and the one i go to is NrothEast of Varrok right out of the city, there are 3 yews here and a couple of people chop here, I don't find it as too many as i do with Fally, or Edgeville. Most efficient place considering its shot walk to bank.
/\/\/\/\/\/\/\/\/\/\/\/\/\______MINING______/\/\/\/\/\/\/\/\/\/\/\/\/\/\
The power house to mining is Coal for money. Tons of people will be buying this. It is the main thing used for Smithing for higher lvl smithers, and those are the people you want to target, but coal dosnt come untill lvl 30 and isnt efficient untill after you have aqqired a rune pick. I find it nessary to have a rune pick to mine coal- But i dont like waiting that much- Now eairly eairly lvl's__ Between 1-25__ i suggest that you just mine tin and copper, then smith it. Don't go to iron yet because higher lvl's use that for steel, and they will have a rune pick. That gives them all the power for this and i promise you they will get 10 ores to 1 of yours. THAT IS IF YOU EVEN GET ONE. Now that your lvl 25 you need to gain a little money. At this lvl you should start mining ess - You will be able to do this after the Rune Mistory Quest. You should switch off between Mining ess and tin and copper. This way you can start saving for that rune pick so you can become a high lvl miner as well. The ess can sell for 30 ea., but YOU GOT TO WAIT. Before you sell. If someone is buying at 30ea. they will want you to sell them a load of ess at once. Again i like the look of 1k. This will gain you a few lvl's with you low mining and almost. Just 2k short of buying your pick. Now just get your mining and smithing up untill the great lvl of 41. Once you get this lvl aquire that last bit of gold you need for your rune pick. Now at this lvl your saying 32K for a pick are you crazy?! But it will pay back its debts fast. Now you got a dicision to make. What path do you want to fallow? You can start mining iron and selling that, or you can mine it and continue to smith. Smithing later becomes very very good for money. While mining starts off just a little bit ahead and stays ahead untill around lvl 70. I suggest that you mine iron untill lvl 45 and smith it. Then if you want to just mine that is when you change over. A good place to get coal at this lvl is at the Edgeville sewers. You can enter this by a house right outside of varrok a little NorthWest, or you can enter it by going to edgeville and walking down a ladder by the yews. REMEMBER IF YOU ARE GOING IN FROM THE HOUSE OUTSIDE OF VARROK, you WILL need a brass key. Now you can start mining coal and taking it to the bank. This is a good way for fast money at this lvl. You should get over 800 ore before selling. Now if your lucky you might find a 175 ea buyer, But most commonly sold for 150ea. You can mine here untill lvl 60 mining. At this point you can go to the mining guild in fally. Here there are tons of coal ore and you won't have any trouble unless it is crouded there.
/\/\/\/\/\/\/\/\/\/\/\______RuneCrafting_____/\/\/\/\/\/\/\/\/\/\
This is a easy way to get money. I pefer this over all others because all u got to do is click every 15 seconds. I'm even Rc'ing as i type this! It gets to be a good profit and i find it a very very nice way to get money. I have made 1 mil this week alone by RC and im just about to hit lvl 51 RC. It is good if you got a lot of friends on. Just talk to them and make your money. It is slow at first. You will have to wait till after you lvl up and can make multi runes per ess. That is another draw back eairly on. Don't buy ess. Mine it yourself, it is a good choice untill you can make 4 airs per ess. Then you can start buying and keeping a profit. Once you got this going you can keep the same amount of money as u had before ,BUT have tons more ess. I stay'd at 400k after selling my airs. But then i brought 10k ess on top of that. I'm about 70% done with the 10k ess and have made over 1 mil off of it. This is GREAT profit. And basically all im doing is talking to friends. You can lvl up untill you can make 8 airs per 1 ess. And if you become fond of this game and dicide to become a member. This lvl will help you out a lot. Then any rune you want you can craft it easily. Stick to airs for a constant flow of cash.
These are the three ways i think are the best to make money.
I left out Maple and Magic logs for Woodcutting.
For mining i didnt leave out much besides some mining spots.
Rc, i left out Crafting laws and nats for money.
This guide is mainly for beginning players or anyone having a little trouble money wise.
Feel free to add on any info you wish to better improve the guide and please, no negative comments

keep the guide up and a nice convo. for all