What you need to overclock your laptop's GPU is first of all a laptop with a dedicated graphics card. Don't bother trying to overclock a laptop with an integrated graphics chip from Intel such as "Intel HD graphics", "GMA 4500mhd" or anything of that nature. Only dedicated chips from AMD or Nvidia are eligible for overclocking.
Different tools are at your disposal for overclocking, and it can (usually) all be done with software solutions. The exception is when the manufacturer has made the unfortunate choice of locking down the card in the BIOS to prevent overclocking. You can use most of the same tools for laptops as those you would use for overclocking a desktop graphics card. You have to keep in mind, however, that the space inside a laptop is restricted and a laptop GPU is likely to overheat faster than a full-size graphics card in a roomy desktop computer chassis.
As for the aforementioned overclocking tools, there are several good ones--even official varieties from AMD and NVIDIA. If you want to browse around, visit Guru3D for a more or less complete list of downloadable software (most of which are freeware). For the sake of this demonstration we will use eVGA's Precision software, which is very easy to use. It's branded and created by eVGA for use with the manufacturer's own graphics cards, but works equally well with other cards and even laptop GPUs.
The simplicity of this tool is admirable; you can adjust the core clock, shader clock and memory clock separately, with an option to link the shader and core clocks (recommended). In most laptops, the fan speed is controlled by the BIOS (the computer's firmware), so this option will be grayed out.
Now you are free to start adjusting those clock speeds, but be careful! Raising the bar to high will cause your system to hang and/or overheat. It's highly recommended that you raise the clocks in small increments and test the system for stability in between the clock increases. You can probably safely raise the clocks by a larger amount, say 50MHz, the first time around, and then up them by 10MHz at a time, testing for system stability between each increase.
Just increasing the clock frequencies of your laptop's graphics card and see whether it hangs or not won't do you any good. Unless you have tried it "for real" you have no way of knowing if it works at all in actual games, and perhaps more importantly if it is a stable overclock, i.e., that it works consistently when gaming for hours on end without crashing or overheating.
A couple of good programs that are specifically designed to stress test your system are Furmark and Futuremark's 3D Mark benchmarks (see Guru3D for these downloads as well). Furmark is freeware and very simple--as the name implies it animates some "fur", which is apparently a tough task for any graphics card.
3DMark on the other hand, is not freeware but available in shareware versions. This is arguably an even better option as it simulates the workings of a real game. It can also be run on a loop, so if your gaming laptop manages to run one of Futuremark's tests for several hours without any issues you have a stable overclock.
You don't just want to know if it works at all or just hangs--you should also watch for artifacts on the screen (strange lines or other quirks in the rendered video), which would signify that your GPU has passed the limits of its ability.
To get an overview of how gaming laptop overclocking works in practice, have a look at this Alienware M14x overclock . This laptop uses the NVIDIA GeForce GT 555M, which is a rather common graphics cards in current laptops. As it turns out, it is possible to push the GT 555M to provide a 20 to 30 per cent performance improvement--one that is clearly noticeable in your games.