I can't do decent ASCII art and obviously can't use real images, but here's how I solve the cube... it's pretty much the way alex.tan described, and it stems originally from the first way I learned (the instructions that came with my first cube, which I memorized in a day or so) but has been modified with quicker moves from a couple other methods. So, here is...

How A Brown Fuzzy Pokemon Solves The Rubik's Cube

I realize this is similar to rubiks.com's solution, but the way I do the last layer is different, so there.

This assumes you're familiar with the very basic properties of the Rubik's Cube, such as there only being one of each piece and the pieces, not stickers, moving around. Oh, and if I mention which way a piece is "facing", I'm really talking about the sticker that's the color of the face you're trying to solve.

If you want to memorize these moves and be able to solve the cube in a couple minutes, watch what your hands are doing. Most of these patterns are quite pattern-like and either easily understood or easily memorized.

Step 1a: Arrange the edges of the top layer. Pick the side you wish to solve first -- I usually use whatever's opposite white -- and call this the top layer for now. Find an edge piece with one side its same color. I'll refer to the piece you're trying to move as the target piece.

• If the target piece is already in position and oriented correctly, good.
• If the target piece is in position but flipped the wrong way, either give the side it's on a quarterturn so the piece ends up on the middle layer or pick another piece.
• If the target piece is on the middle layer... Turn the side that does NOT have the top color's sticker adjacent to its center. This should put the correctly colored sticker next to the top center piece.
• If the target piece is on the bottom layer facing DOWN, just give the side it's on a halfturn to put it in place.
• If the target piece is on the bottom layer facing OUT, give that side a quarter-turn either way to put it on the middle layer and go from there.
Repeat this for the other three edges, but be sure the egdes go in the correct order. If you need to, align the edges you already have with the centers on the sides so you can see where the edges are supposed to go.

Step 1b: Arrange the corners of the top layer. The concept here is what seems to stump most people who pick up the cube... every time you move a piece, you move others out of position. The trick is to figure out how to break up what you have, place the piece you want with one of the broken bits, and put it all back together. Doing the corners is one of the easiest ways to do this; in fact, go try it now. Or just find a corner you need, find the two edges it fits between, and...

• If the target corner is on the top layer but oriented incorrectly or just in the wrong spot, give one of the sides that share the corner a quarter-turn so the corner ends up on the bottom layer, give the bottom layer a quarter-turn either way, and turn the side you moved back where it was. Try to keep the target corner from facing downwards.
• If the target corner is on the bottom layer facing DOWN, either pick another corner (please) or do this: Turn the bottom layer so that the corner is directly below where it belongs. Give the bottom layer a quarter-turn either way. Half-turn the side that contains both the target corner and its home so they switch places. This moved one or two pieces out of position. Now, turn the *other* side that now contains the target corner so the corner moves AWAY from the side you just turned. Give that other side another half-turn, and restore the target corner. You may have moved a corner out of place; fix it if you did.
• If the target corner is on the bottom layer facing OUT... well, this only requires three moves, and is left for you to figure out ;)
You should now have an entire layer complete, meaning that you have an entire side one color AND that the three squares on each side that touch the completed one are the same color. Turn the top layer so that these sets of three squares all match the centers on the sides, and turn the entire cube over so the solved face is now the bottom. Now it gets fun :)

Step 2: Finish the middle layer To complete the middle layer, simply find the four edges that go around the center one at a time in the top layer. Turn the top layer so your target edge's side color matches the side center it touches, and using this side as the front...

• If the target's home is on the right, perform the moveset `U R U' R' U' F' U F`.
• If the target's home is on the left, perform the moveset `U' L' U L U F U' F'`.
• If the target is in its correct location but twisted incorrectly, or several edges are switched, use one of the above sequences to move a piece out and put it back in correctly.
That wasn't hard, was it?

Step 3: Orient the edges on the top layer Looking down at the top this time and using it as the front, this step hinges on the simple sequence `R' F' D' F D R`. You'll need to use it a maximum of three times, usually only once. If NO edges are facing upwards, just use it. If two OPPOSITE edges are facing upwards, turn the top/front so they're oriented horizontally and then use it. If two ADJACENT edges are facing upwards, turn the top/front so the corner between them is in the upper-left and use it. Now all four should be face-up.

Step 4: Position the corners Turn the top layer until the colors on *exactly* two corners match the colors of the sides that share them. If they're adjacent corners, turn the cube so they're both on the left side and again using the top as the front, perform `L F' R' F L' F' R`. If they're opposite each other, perform the same sequence, then find the now-adjacent corners and do it again.

Step 4: Orient the corners You'll need two sequences here. Again, the top is considered the front for ease of explanation.

• To twist the corners CLOCKWISE, except the one in the lower-left corner, use `R F R' F R F² R'`.
• To twist the corners COUNTERCLOCKWISE, except the one in the upper-left corner, use `R' F' R F' R' F² R`.
You may have to use these sequences a few times before you get the hang of them. When you're done with this step, the top *face* should be complete, and the only pieces in the wrong places should be the four top edges.

Step 5: Fix the top edges The cube may be complete now, but odds are it isn't. Most of the time you'll have three edge pieces shuffled around, in which case you should use one of these two sequences. In both cases, the front is the top and the edge you don't want moved is on the bottom.

• To shuffle the edges CLOCKWISE, except the bottom one, use `U² F R L' U² R' L F U²`.
• To shuffle the edges COUNTERCLOCKWISE, use `U² F' R L' U² R' L F' U²`.
If all four edges were swapped, use either sequence with any edge on the bottom. Now only three are switched.

Congratulations! You have just solved the Rubik's Cube.

This method is a bit redundant at times, but I've found it has very few sequences to remember while not being very complex. If some of the above is incomprehensible, I apologize; describing the cube is difficult in words. Please tell me what you don't understand so I can clarify.

I can get a consistent two minutes using this method, although there are a couple other slightly sequences I use when I can remember them. If you want to be an utter maniac and do the cube in under 20 seconds, search Google for speedcubing or something similar and have a LOT of free time. Then come laugh in my face because you're faster than me.

thus ends Eevee's Cube Method v1.0

addendum: yes, taking the cube apart DOES bother me, but not nearly as much as people who casually babble on about how they "solved" the cube by TAKING THE STICKERS OFF AND REARRANGING THEM. At least disassembling the cube requires some effort and thought; taking the stickers off accomplishes nothing but making the glue less gluey, especially since the person who does it will probably have the cube rescrambled within three minutes.