It's not just your CPU you could be getting more from!
Just as overdocking your CPU can help you inch your gaming performance ahead slightly, overclocking a GPU is one way to squeeze extra frames out of a graphics card, whether that's because it's starting to flag with age or because you know it can do better than the manufacturers think is fair.
Of course, overdocking your graphics card isn't a free pass to superior performance. Performance improvements can be minimal even when you get them and, as with all kinds of overclocking, you have to take care with what you do otherwise you can physically damage your graphics card. It's not for the faint-hearted, and it's worth pointing out that any advice we give here should only be followed if you're comfortable knowing that you risk breaking your card completely.
If that doesn't put you off, however, and you want to tinker a little with your hardware, overdocking is a great way to have some technical fun with your PC. And let's face it, isn't that what we're all here for?
Beginning
In the past, overclocking a graphics card meant you had to know a lot about how the card worked, specifically how to tune the voltage and GPU core clock speeds. Luckily, the arrival of DirectX 11 (and subsequently DirectX 12) has put overdocking well within the grasp of most lay-users. You don't have to have a degree in electrical engineering to do it anymore.
The reason for this is that a pair of technologies - AMD's PowerTune and Nvidia's GPU Boot - mean that turning up the voltage and clock speeds together doesn't have the effect it used to. These days, it makes more sense to increase the voltage and let the card's own firmware and drivers worry about the clock speed. This prevents the GPU cores from artificially lowering their own clock speeds (throttling) because they're running beyond the manufacturer's stated power levels. The whole reason those limits exist is because the manufacturer wants to prevent the GPU temperature getting too high - but if you're using an aftermarket cooler, for example, it won't be a problem - unfortunately, the card doesn't necessarily know that.
In any case, to start overdocking, you need to get the right software. Most CPU overclocks are done from within the BIOS, largely to prevent instability and data loss from within Windows, but GPUs can be edited and controlled without a reboot. Most card manufacturers offer their own tool, but because the software interacts with the GPU you aren't necessarily restricted to that tool.
To explain less abstractly, Sapphire's Trixx tool can be used on any AMD or Nvidia GPU Sapphire supports, even if the card itself was made by another manufacturer. The same is true of MSI's Afterburner tool and Asus's GPU Tweak. This means you can use any tool you feel comfortable with.
MSI's Afterburner is currently the most popular, so we'll refer directly to that. If you use another tool, though, you shouldn't have a huge amount of difficulty figuring out which settings are the equivalent.
Benchmarking
First, download and install Afterburner (gaming.msi.com/features/afterburner) and the RivaTuner Statistics Server it comes packaged with. The default skin is a bit much, so click the settings button (it's a cog icon) and find the 'User Interface' tab. We've selected the Afterburner v3 Skin, but you can choose whatever you like.
Next, you need to enable two settings: in-game overlay and framerate monitoring. You'll find these in the 'monitoring' tab in the settings dialogue. Click the tick mark next to 'framerate' then below, tick the box next to 'Show in On-Screen Display'.
Now test your card's speeds to create a benchmark. You can load any game but we've chosen Minecraft. The frame-rate will appear overlaid in the top left of your game in purple numbers, allowing you to check the average speed. Make a note of this (you can also check the performance graphs) because this is the speed to beat. Also keep an eye on how the temperature and fan speed graphs look, because the closer to capacity they are, the greater the chance of your card being unable to take more overclocking.
If you want to be a little more scientific, you can use an actual benchmarking tool, but it's not required.
Overclocking
Now you know what you're trying to improve, it's time to actually improve it. Begin by increasing the power limit. You can move this all the way up - the artificial limit is there to prevent the card getting too hot, but it's usually a conservative estimate, and in any case there's a separate temperature limit.
Now you can use the Core Clock slider start actually increasing the GPU's speed. Do this in small increments of maybe 5-10MHz, clicking 'apply' and then testing your card with every change. If you experience no problems, do the same with the memory clock. Once you start getting graphical artifacts or unexplained crashes, take both of these settings down a little. That's the fastest speed for your overclocked card: just before you start seeing problems. Note that the Core Voltage will be taken care of by the card. Don't interfere with this unless you know what you're doing!
If you're not sure about the numbers, try googling your card and seeing what the average overclocked settings should be. Every individual card will be different, but you can at least get a ballpark figure! In MSI afterburner, you can save a profile, so you might want to save a specific overclocked setting so, If you ever want to put the card back to how the settings were, you can hit the 'reset' button.
Monitoring
Obviously, from this point on you have to be careful about your card's temperature to prevent damage, though be aware that any increase in temperature will shorten the lifespan of the card. Don't be too concerned - when's the last time a graphics card died on you, after all - but be aware that the faster and hotter it runs, the less time it'll run well.
If you are overclocking and don't have an aftermarket cooler, it's always worth looking into one. The card will naturally get less stable as it gets older anyway, and newer games will start to make greater demands on it. Just because it's fine with your current set of games, it doesn't mean it always will be - if you start seeing graphical glitches, quit your game and remove the overclock. It may not fix the problem (if the card is actually damaged) but at least it should prevent it from getting any worse.
Other than that, you're free to experiment and to enjoy the faster speeds on offer with your overclocked card!