The Basics
Ok first of all, woodcutting is probably one of the easiest skills to get up, and it can also be the most rewarding...
Equipment
To start of your going to need an axe, first you should get an iron axe, from the Grand Exchange or Bob's axes in Lumbridge.
When you get your woodcutting level higher, buy the axe that matches your level, for example... Your 21 woodcutting, so buy a Mithril axe.
Keep buying the axes from the Grand Exchange, that is probably the best place to get them.
1-30
Ok, 1-30 is pretty easy, there is pretty much only 2 good places for these levels...
F2p: Around Lumbridge and Draynor.
P2p: Around Catherby and Camelot.
Ok lets start in F2p... First off, equip your axe and go cut trees until 6 woodcutting, buy a Steel axe from Bob's Axes and then go cut Oak's until 30 woodcutting.
Now for P2p... Do the same but do it in Catherby and Camelot.
30-60: Now there is again, different ways for F2p and P2p...
F2p: Cut willows at Draynor, to get to 60 will take about 2-3 days playing about 3 hours a day.
P2p: Cut willows at Draynor, Catherby or Barbarian Outpost... The fastest way to get to Barbarian outpost is by using a games necklace (charged) and teleporting with it, there is a bank deposit inside the building where you can deposit your willows, they will go straight into your bank.
60-99
Congrats, your now getting pretty good at woodcutting, you can cut Yews, but I don't recommend it, because they are very slow and they only make about 30k an hour at lvl 60 woodcut.
Anyways... 60-99 Woodcut takes about 2-3 months of solid woodcutting, it takes around 180k willows to get there.
F2p: Continue cutting willows at Draynor, this is the best spot in f2p when its not so crowded.
P2p: Keep cutting willows at Barbarian outpost, if you want to buy a Dragon axe at 61, thats good, although they are not much of a difference but they still count... D Axes cost around 2.9M. Now there is also another way that people get 99 wc in p2p, and thats by cutting Maples at around 80-85 all the way to 99. You can try that but I don't really recommend it.
Some people stop cutting willows at 90, and move on to Yews, you do start cutting yews fairly fast at this level but willows are still the best exp in the game for you. Doing Yews from 90-99 will make you quite alot of cash though, and thats why some people do it.
Conclusion
Once, or "if" you get 99 wc, go to Lumbridge and talk to the woodcut tutor, he will tell you that you can buy a skillcape of woodcutting off of him for 99k (99,000gp). Well done, now have a party :)
