Rubik's Cube for Beginners
You don't need to learn more algorithms to get faster. The beginner method can actually get you pretty far. I can average under 30 seconds with the beginner method and I am sure there are faster people.
Get a good speedcube.
Your cube should be easy to turn, or else the rest of this guide will not apply. A bad cube locks up and gets stuck frequently. If you have a knock-off cube, chances are yours falls in the bad category. There are certain knock-offs that are not so bad, but if you are just starting out, an official Rubik's cube is good enough.
I myself started with a knock-off. After learning the beginner method, I was able to drop my time down to 90 seconds but I could not get any lower. Then I got an official Rubik's cube, and immediately my times went under a minute. I had been wasting half a minute on each solve because the knock-off was so hard to turn.
What will help a lot is if you lube your cube. If this is your first time hearing the advice, it might sound a little crazy, but I am serious. Make sure you use a silicone based lubricant and avoid WD-40 and other petroleum based lubricants. For a more thorough guide on how to apply the lubricant, you can check out Trevor Holland's page. That page is archived so the pictures are not there anymore, but Gilles Roux has some nice pictures at the top of the page.
"Go slow, look ahead."
This is probably the most important advice of speedcubing. It is definitely one of the factors that singles out the top cubers in the world; the best people have mastered this advice.
All the pauses in between steps pull your time up. Imagine that you pause for 2 seconds after each step. (Here, each individual corner in the first layer is considered a "step." Same for the middle layer edges.) Then you wasted 24 seconds in your entire solve doing nothing.
To eliminate these pauses, you have to look ahead. The only way to look ahead to go slower. This may sound contradictory, but the time you save by not pausing is much greater than the time you use up for going slower.
How do you look ahead? When doing one step, you should be anticipating the next step already. While you are forming the cross, you should be searching for the first corner to insert. When you finish the cross, you immediately proceed to insert that corner. While you are inserting the corner, you should be looking for the second corner. This pattern continues until you finish the first two layers.
Because the third layer is completely algorithms, it is not easy to look ahead. Instead, you should slow down at the end of each algorithm so you have a sense of the next state on the cube.
Short (and useless) anecdote: In my world history summer class in 2007, the teacher gave us a lot of free time. I taught some people how to solve the Rubik's cube and helped others improve their times. I gave one of my friends the very important advice of going slowly and looking ahead. Unfortunately, I phrased it in a very paradoxical way: "To get faster, you must first go slower." She started to laugh really hard. I started to laugh too, when I realized how I turned a serious advice into a joke. Is there a moral to this story? Not really, but I thought it was a fun incident to share. Just remember that this is no joke. (Hopefully I did a better job presenting this advice on this page than I did in that class.)
Learn "finger tricks."
Certain sequences of moves, such as [R U R'] can be executed very quickly if you know how.
Make sure you can execute the last layer algorithms quickly.
Since the last layer is mainly "identify the state - execute the algorithm - identify the state - execute the algorithm, etc.," you want to be able to execute the algorithms quickly.
There are many videos on the web accompanying the algorithms. For example, Katsu's Planet Puzzle has a video of the algorithm for Step 6 - State 1. (The diagram is different but the moves are the same.)
Minimize whole cube rotations.
Whole cube rotations waste a lot of time because you have to regrip and accomplish nothing in the process.
For the cross, rotations are unavoidable.
How to avoid rotations in steps 2 and 3 is in the next tip.
For the last layer steps, instead of turning the whole cube to get the correct starting position, I find it much quicker to do U and U' moves. However, for the very last step, cube rotations are fine, so that you can end the solve right after finishing the algorithm.
Learn to do steps 2 and 3 from all directions.
Remember that these steps are not algorithms. Although in my guide, I only show you how to insert a first-layer corner into the RF slot (intersection of R and F faces), doesn't mean that you have to use that slot each time. If the corner needs to go into the BL slot, you don't need to rotate the cube so that the BL slot becoms the RF slot. Just insert it directly into the BL slot.
If you truly understand the move sequences, you should be able to insert a corner into any of the four slots. The same principle applies with the middle-layer edges.
Inserting corners and edges from all directions might feel weird at first, but with enough practice it will become much easier.
Practice, practice, practice!
Just reading these tips isn't enough! You need to practice so that the strategies become second nature.