DS seems specifically designed to trip you up and, in some cases, the #variables/#equations shortcut will be exploited (I've seen this numerous times). For example, they may have x+y=3 and 2x+2y=6. There are two equations, but they are the same equation and so together they are insufficient. Other times there may be 3 variables and 2 equations, but one can be factored to eliminate or aggregate variables. For example, if provided with (x+y)*z = ? (3 variables), one choice might say xz+yz =50. Three variables and 2 equations, but that choice would be sufficient.

Perhaps if you keep in mind the fact that the GMAT is exploiting these common trip-ups, you can weed them out more effectively. I generally approach each DS question with the following steps:

1) Understand what is being asked and rephrase the question if necessary. For example, if it asks whether -x > 0, it's easier to think of it as whether x < 0.
2) Immediately factor any equations in the question so that they are available in different forms. For example, if you have a question pertaining to (x+y)(x+y), immediately write down x^2+2xy+y^2. Keep the alternate forms handy to reference when evaluating the answer choices.
3) Take a high-level view. Spend a few seconds looking at what the question really means. For example, a question may ask whether (x-1)(x)(x+1) is divisible by 6. You will want to understand that it is asking whether a set of 3 particular, consecutive numbers are divisible by 6. This may allow you to apply some tools pertaining to consecutive numbers.
4) Before submitting the question, look back at it and verify that you have answered what was actually asked. If it asks to verify x and you verified y, then you've made a mistake.

It took me a while to realize it, but DS tests something completely different than problem solving. It tests your ability to understand a problem rather than to just work through it.

Inkybinky has given some strong tips for approaching the whole category of data sufficiency. I thought I would give you some ideas for one of the two main types: specific number.

Here are some tips for addressing the type of data sufficiency problem that asks you for a specific answer. For example, "what is the value of x?" or "How many square inches does the rug cover?" These questions account for about 75% of data sufficiency questions and are generally easier for students to understand than are the other type -- yes/no data sufficiency.

THREE WAYS TO BE SUFFICIENT WITH SPECIFIC NUMBER QUESTIONS

With specific number questions the key to finding the best path to determine if the statements are sufficient is to understand what you bring to the problem. There are several things you can bring to the problem:

1. Get two equations for two variables - This usually only works for word problems
The key lies in the information that you supply for each question. In the first type of question, the word problem, you often supply the equations. If you do supply the equations then this is probably the path to finding the correct answer. As "InkyBinky" mentions above, they will fool you with this - if they supply the equations treat this like a stranger offering you a drink in the bar = don't take it!

2. When you have to supply the formula such as with work/ rate, geometry, and percentage increase problems- figure out ahead of time which clues you need.

In the second way to be sufficient, you supply the formula, so that knowing the information that is required by that formula is vital to solving the problem. You may for example need to get the measure of an arc, so the clues you need are the diameter of the circle and the central angle. If you think about this ahead of time you can then just verify that the statements give you the needed information.

3. Actually get one specific value. This is usually the way to solve algebra problems that are not word problems, in other words, algebra problems that actually give you the equations. Be careful on these questions as they are often tricky.
In this case, you will need to actually find, or at least know that you can find a single value - a specific number. Often the two equations will provide you with different ranges or sets of possible numbers and you will have to see if you can get down to just one value.

I hope it helps!