Train your woodcutting. In order to cut yew logs, you have to get your woodcutting to at least 63 because it takes lot of time to cut yew logs if try when your woodcutting level is only 60.
To get your woodcutting from 1-20, cut down normal trees south of the Grand Exchange, bank them, and sell them after you reach 20 woodcutting. Normal logs sell at a very fast rate.
To get your woodcutting from 20-40, cut down oak trees west of the general store in Lumbridge. They sell a bit slower and are priced lower, but it is worth it to sell them and make decent money.
To get your woodcutting from 40-60 (other methods are 40-65, 40-80, and 40-99), cut willows south of Draynor, and bank them. Once you get to level 80 woodcutting, sell every willow log you have in the Grand Exchange. You can also cut them east of the Lumbridge general store and when you get a full inventory, sell them at the general store. Because the nearest bank is far away, it is not worth the time to rush to the bank and come back to the spot here.
As you improve your woodcutting level, buy better hatchets to increase your rate of speed. The profit you make from woodcutting level 1 to 60 can buy you a steel, mithril, adamant, and rune hatchets all at once.
Go to world 1. The yews respawn the fastest in that world (60 seconds) But there is a disadvantage if you go world 1 there will be a lot of people who are cutting yews too. Other good worlds to go to are worlds 3 and 4.
Pick your spot. The best places to go are east of the Grand Exchange (there are three yews there), near the church in Varrock, and south of Falador. The one west of Lumbridge is good too but there are no banks nearby. The best for members is south of seers village. Bank in catherby bank. This is usually really crowded but there is a way you can get past that. Go to the runescape homepage and at the top click a German flag. Then the site will be German. Click the play button and when you get to the login screen go to the world select. Click the members world with the least amount of people. When I play runescape on these worlds there are usually 10-20 people on a server. VERY good. Click that and there will most likely be no one there.
Store them in a bank. It wouldn't be wise to sell it directly in the Grand Exchange. Wait until you have a certain amount that you want. Good choices are 500 (235.5k), 1k (507k), 2k (1.014m), 3k (1.521m), 5k (2.535m), 10k (5.07m), 25k (12.675m), 50k (25.35m), 100k (50.7m), 500k (253.5m), and 1m (507m).
Sell them in the Grand Exchange - not anywhere else. The general store rips you off by a ton (you can only sell it for about 100gp when there is none), and there is no woodcutting shop in F2P.