First off if you are over level 100 you will want to go to part 2 of this guide. This method is one of the quickest ways to level up woodcutting, but even with that it still takes a while to level up.
Here are the mcmmo xp rewarded for cutting trees per log:
Oak: 10 xp
Birch: 50 xp
Spruce: 50 xp
Jungle: 33 xp
(These stats are doubled for [VIP] players)

Let's get started, shall we?
------
Part 1 (Levels 1-100)
-----
     Although I say "Levels 1-100" It can be used for any level, and I personally would recommend you use this method until you reach level 150, but level 100 will be satisfactory for part 2. I will also warn you this is probably the slowest part, so be prepared to spend lots of time cutting on this part.
     Let's begin the method now, shall we? So to begin you will need the following
- An axe (preferably diamond)
- Many saplings (Any type, Preferably birch or oak) (Somewhere around 640 per daily trip will suffice)
- Bonemeal (Equal amount to your saplings)
- Dirt (If in a desert)
- Cobblestone or any non valuable block you're willing to place
     Now that you have these items, look for an area thats relatively clear (It can be in the desert, but you must bring dirt). Now here is where you get to choose your sapling. Heres the guide for Oak Saplings:
1. Make a row of dirt going in any direction however long you want (I recommend 64 blocks).
2. Place a cobblestone block 7 blocks above (six blocks of air inbetween) the dirt on one end of the row.
3. Continue the blocks above your dirt row until you get to the end of it, so every dirt block you plan to plant trees on has a cobblestone block above it.
4. Plant saplings in your row of dirt
5. Use bonemeal on every sapling, it should work for oak saplings, it may take a bit holding down right click.
6. Cut down the trees
7.Repeat
Additional:You may want to add two extra blocks on each end as "endpoints".
Here is a picture example:
     
     You should be able to plant, grow, and harvest a row of 64 in above 5-7 minutes. Also the blocks above the dirt are important so that your trees can not grow overly large and become annoying as well as more time than they're worth. Once you do that you want to make at least one more row equivalent in length to your first, using the same exact instructions. This is to let the leaves decay, because it's harder to grow trees on a row with a ton of leaves, also it allows you to recollect some saplings. You want enough rows so that at least one row is clear or in use at all times. For example using a diamond axe with efficiency 4, I had 3 rows of 64. As shown in this picture:


Here is the guide for Birch:
1. Make rows of dirt, but with two blocks of space in between each dirt block. You should have a total of 64 trees in a row. (That's 192 blocks long, you can chop it down to 96 if you make two rows within 2 blocks of each other with 32 trees instead of 64)
2. Plant saplings in the dirt spots.
3. Use bonemeal
4. Harvest Trees
Optional: Set the 7 block boundaries like in the oak farm, this will just make every birch tree the same size, no other benefit.
Here is an example of a small birch tree farm:


     There is no real "winner" to the best method, as it is faster to cut oak logs, but birch logs give 5x the experience. So you need to determine which method is the best. I used the Oak log method, but I have seen success in the Birch log method as well. Some ways to up the speed of the cutting include:
- Enchanted Tools
- Haste buff (Or another useful buff) from a beacon
- Continuing to get faster at the cycle of each method.
Finally, part two, at long last, what excitement could we have here?!
------
Part 2 (Levels 100 (150) +)
------
     This is where you start to get levels to come in very quickly. I went from 200-400 in about half the time it took to get from 1-200.
Here is what you need:
- Bonemeal, don't go overboard but 3 stacks is usually enough for my day.
- 1 or more diamond axes (One diamond axe per every 3 jungle trees should suffice, *DO NOT ENCHANT THE AXE*)
- Diamonds
- Jungle Saplings
- An Iron block (If repair level is over 50)
- A chest... or two... or three...
-A crafting table

    From the materials I think you can guess what's coming next. It's time to abuse Tree feller. For those who don't know Tree feller is an mcmmo ability that can be activated by right clicking on a log then breaking a log. First off you might as well build a small shack or base of operations. In this shack put your iron block, crafting table, and chests.
An important note is that your space of working needs to be in a non snowy biome. Otherwise the trees will not grow! Let's get started on the step now.
1. Make several 2x2 spaces of dirt to grow your trees. Space these out at least 4 (but not over 7) blocks apart from each other. If you are level 100 you have 4 seconds of tree feller to cut down multiple trees with, so you can probably get around 3 trees in that time. However if you are level 300 or so, You can probably down around 4 or 5 trees. And
the pattern goes on.

2. Plant Jungle saplings in the 2x2 spaces, make sure you have a 2x2 square of saplings on the dirt space.
3. Use bonemeal on all of your trees.

4. *READY YOUR AXE*
5. Cut the trees from the bottom block as fast as you can, If your diamond axe loses durability (Down to red), switch to a second one quickly if you brought it. Each axe can cut around 3 trees (may vary).
6. Collect tons of logs (3 trees would give around 3-4 stacks, 6 trees give around 7-8 stacks... and so on)

7. Repair axe if level 50+ in repair (See Repair Guide here: http://www.noobscraft.com/guides/repair-guide!-(pictures-included!)/msg56003/#msg56003), Otherwise make a new axe.
8. Repeat the cycle, Each tree gives about 2000(small) - 6000(Very large) xp. (Equation: (Tree Height*4)*33)

     With this method you will be AFK alot. So you will need a 3 minute activity to do while you're waiting if you don't want to stare at a timer. I personally watch videos, play around on forums, or play another game. But figure out what you want to do.
     
     Continue this process until you have enough wood, are satisfied with your level or you just feel like you're tired of it and want to take a break by making a guide about it... I mean, you're tired of it. I hope this helps people level up in the arts of the Woodcutting, and make some money on the side as well. Happy Woodcutting!

***UPDATE February 8, 2013***
With recent changes to Mcmmo you actually don't need to worry about growing trees "too large". You can also grow trees easier (takes less space). But branches are not broken with tree feller, so you will have a lot of pointless floating branches. These should not effect you at all, even if the seem abnormal, you can still grow trees like normal, and it's more of a good thing than a bad thing.

***UPDATE Februrary 11, 2013***
The levels 100+ method has been completely nerfed, not only are tree "too large" back, but you have a lot less total Tree feller seconds. You can still attempt this method but now it will be a lot harder to get the same experience or money profit out of it.

***UPDATE March 2nd, 2013***
The level 100+ method works effectively once again! Fatnoob went ahead and changed mcmmo a bit, and now you can use the method once effectively as ever! Happy woodcutting!

Yay! Thanks Mac! For the longest time I thought jungle gave the most xp. And for the 2x2 Jungle method, if you already set up a Haste beacon, changing it to Speed might be helpful.

I didn't learn that for myself until I made this guide and tested it out.