Tips and Practice Techniques

Many of these were introduced to me on Japan Speed Cubing Club and the Yahoo! speedcubing forums.

Buy/Make/Maintain a Good Speedcube

For durable stickers, I recommend Cubesmith. Serious speedcubers should learn to create and maintain a speedcube that best fits his solving style. Experiment with several top cubes (see speedcubes.net), different screw tensions, and different lubricants (silicone spray of various brands (Tempo, SNAP, CRC, Jig-a-Loo), shock oil of various weights, etc). WD-40 quickly wears out the plastic; good speedcubes should not need it. (Leaving WD-40 on a very tight cube for a few days may make it tolerable, but it would never become a good speedcube.) Disassemble and clean out the dust inside the cube once in a while. Gilles Roux has a helpful guide on lubrication with pictures. With some brands of silicone spray, it can help to completely disassemble the cube, remove excess lubricant with paper towels, and blow-dry.

Exactly how much to lubricate is each speedcuber's choice. Very lubricated cubes will allow faster execution for last layer while less lubricated (but smooth) cubes can help looking ahead during F2L. It's also a good idea for competitions to use a cube that almost never POPs.

I lube my cube every three months or so and usually about two weeks before any competition. From that point, I play with each lubed cube to make sure that the lubricant sinks in and the cube is not too slippery. Although slippery cubes let you turn more moves per second, you are more likely to lose control and make them lock up than with a less-lubricated one. For loss of just a bit of speed, you can gain a lot of accuracy and look ahead much more easily, which is very important.

Inspection and Cross

Learn your color scheme by heart. From the center colors of any two adjacent sides, you should be able to immediately tell the colors of the other sides.
Taking as much time as needed for each scramble, form the cross in 7 or less moves. You should be able to do this over 99% of the time.
Repeat 2, but solve the cross blindfolded. Practice until there are no mistakes.
Repeat 2, gradually decreasing the inspection time until you can always read the cross in 15 seconds. Once you get faster, you don't need to always follow the 7-move rule. Some solutions will be slightly longer but easier to execute.
The transition from cross to F2L is important! This is where even fast cubers have to stop most often ("cube amnesia").
Slow down during the cross to prepare for the first corner-edge pair of F2L. You may want to avoid using finger tricks for the cross to help look ahead.
Solve without preinspection. This forces you to slow down and lets you move from cross to F2L more smoothly.
Form the cross in such a way that, when it is completed, it ends up where you want it during F2L. This eliminates a cube turn before F2L and also helps the transition. (There are a few top speedcubers who do not do this.)

F2L

Before you even start learning full F2L, read my article Getting Fast with an Easy Method.
If you've just started learning, try to make sense of each "algorithm" and group similar algorithms together. Not only will this help with memorization, but also an intuitive understanding of F2L is essential for looking ahead and using advanced tricks.
Reduce regripping as much as possible. This requires, among other things, being able to perform each "algorithm" from every direction.
Find your perfect style. Some like to keep the centers fixed; others use a lot of double layer turns and tilts (this is what I do). Watch speedcubing videos and learn how fast cubers handle F2L.
OK, here's the best speedcubing advice anyone can ever give you: GO SLOW, and LOOK AHEAD.

GO SLOW, and LOOK AHEAD!

GO SLOW

and LOOK AHEAD!!!

Guide to F2L Look Ahead

It's very difficult to anticipate the OLL effectively. Finish the final pair as fast as possible. You will need to stop to recognize the OLL anyway.

OLL

Learn to recognize every case from only 2 sides.
For the easier cases, learn to solve from all directions.
Don't rush. You still have one more step.
Try to use algorithms that end with the last layer on top so that there is no need for whole cube turn in the transition to PLL.
Learn some COLL. Use only the ones you can execute quickly.
Time yourself doing all 57 algorithms in a row. Get faster.
Last layer is just recognition and fast execution...practice, practice, practice!

PLL

Watch videos of fast cubers and imitate. PLL execution videos are great for this; check out Yu Nakajima's. You can use download YouTube videos with this tool and slow it down using VLC media player.
Again, learn to recognize all patterns from only 2 sides. (This is something I should work on myself.)
Again, for the easier patterns, learn to solve from all directions.
As you're making those last turns, be thinking about putting down the cube and stopping the timer. Take this into consideration when choosing algorithms.
Time yourself doing all 21 algorithms in a row. Get faster.
Periodically check the Yahoo! group for better PLL algorithms. Use ACube to try to find better algorithms.

Overall

Videotape yourself and compare your solve with that of fast cubers.
For inspiration, talk to fast cubers online. Better yet, live close to a fast cuber. =)
Learn other aspects of the cube other than speedcubing - cube math, blindfold cubing, FMC, etc.
Take every chance you get to cube under pressure.
Participate in online contests.
Experiment starting with block methods like Petrus and Roux. The point is to have a good variety of opening strategies to handle special cases. Opposite cross is also worth a try.
I heard this one from Ron: have one scrambling algorithm and its full solution using your normal method memorized. You can see how nervous you are by comparing your time with your average for the scramble.

Memorizing Algorithms

CFOP requires one to memorize about 80 algorithms. Here are some things that can make the process less painful.

Relate patterns to one other, by shape, mirroring, inverses, finger tricks, etc. Breaking an algorithm down into smaller substeps or two other patterns is also useful.For example, #12 on my list is #45 twice with a y in the middle. While learning the algorithms, always keep a print-out page handy for reference. Feel free to edit mine by putting in your own algorithms.

One good technique for memorization is to find key shapes or blocks of colors while excuting an algorithm. For example, in doing RUR'URU2R', look at the block formed by the FRD corner and the FR edge. As you excute the algorithm, this block moves up to the top layer and is rotated clockwise 90 degree at a time before being placed back by a 180 degree turn and into the starting position. It becomes much harder to find these things for a longer algorithm, but knowing something peculiar about an algorithm help you reconstruct it as you go.

Another basic method is to "chunk" each algorithm into smaller pieces that can be excuted in one move. Each chunk should be easy enough to memorize, andthen all you need to do is to piece them together to reconstruct the entire algorithm. Chunks can be any finger trick like RUR', R'UR, or B'R'U.

Mnemonics can be useful for getting an algorithm to at least stick in your mind before getting it internalized with muscle memory. Some people associate each move to a sound so that an algorithm becomes a "word." While they can be helpful, these systems should only be thought of as training wheels. Speedcubers need to be able to react instantaneously to any learned case, so the memory needs to be in the muscle more than as letters or sounds. Also, splitting up the moves by soundusually gives a different result than the grouping based on finger tricks. Here's an analogy: mnemonics for a foreign language. I often use creative connections to learn new words, and that fine for taking vocabulary test in class. But it's not as useful in conversation, where I have to come up with words very quickly and put them together in a natural manner--kind of like finger tricks in speedcubing.

Of course, there's always repetition. This could be simplified with the help of a training program like the last layer trainer.