I recently bought Skyrim on PC. It worked fine for a day or 2 and then my FPS got a huge drop to around 15-20 fps. When I checked, it turned out that Skyrim was using my integrated crappy video card (intel HD graphics family) over my relatively powerful dedicated gaming card (GT 540M). This is characterised by your integrated graphics card showing up in the "Graphic adapter" box in the options settings in the Skyrim launcher with no option for your dedicated graphics card. Also, if you think Skyrim isn't performing as it should, you should check this as well. After some googling, I noticed there were a handful of people that have these problems. They suggested these solutions, which usually worked for the majority of the people. I'm going over them anyway because it might help people. THERE IS AN OTHER SOLUTION WHICH HAS PROVEN TO WORK FOR ME, IF YOU HAVE TRIED THE METHODS BELOW, SCROLL ALL THE WAY DOWN.

Before starting, make sure you have updated your driver. Nvidia recently released a new driver which can optimise Skyrim completely.

http://www.geforce.com/Drivers/

1. Going in the control panel and forcing Skyrim to use the dedicated card.

a. Right click on your desktop
b. Go Program settings, located under 3D settings
c. Click Browse and select Skyrimlauncher.exe located in your Skyrim folder (usually Program Files x86/Steam/Steamapps/Common/Skyrim)
d. Change your preferred GPU to High Performance Graphic Card (or something like that), in this case your dedicated card.
e. Do the same for your Skyrim.exe file just to be safe, since that's the main game. Might be that it won't even select it, in that case you're safe.
f. Click APPLY for both.

Check your launcher again. If it didn't work, check the next solution.

2. Going in the ini-files and manually adding your device

a. This is done by going in your Skyrimprefs.ini file, usually located in MyDocuments/Games/Skyrim.
b. Make a back-up copy of this file in case anything goes wrong.
c. Locate the part [Display]
d. It should look something like this, located between bFloatPointRenderTarget and bFXAAEnabled (otherwise use search to find "SD3DDevice")

bFloatPointRenderTarget=0
sD3DDevice="Insert your integrated graphics card"
bFXAAEnabled=1

If your integrated graphics card is noted in the above example, change it to your dedicated graphics card. In my case:

bFloatPointRenderTarget=0
sD3DDevice="NVIDIA GeForce GT 540M "
bFXAAEnabled=1

Make sure you save again and check again.

If this still doesn't work, you can always repeat these steps but then with the Skyrim.ini file, but I really doubt it would help.

If it doesn't work you have probably run into the same problem as me. I really recommend skipping the next solution since it hasn't proven to work and will probably mess up your computer and resolution.

3. Disabling your integrated card (NOTE: This is very risky and I really don't advise doing it.)

Done by right clicking My Computer>Properties>Device Manager and finding your integrated graphics card and disable it.
I really do not recommend this unless you know what you're doing, it might seriously mess up your PC,leaving you to not even getting to start up your PC.

If above solutions don't work, use this

Unfortunately, above solutions didn't work for me. Turns out there's a certain conflict between DirectX and Optimus (the control panel used by Nvidia), or so it seems.

The source of the problem is the d3d9.dll file. This file was located inside my Skyrim folder, with my Skyrimlauncher.exe, ect...
It seems that untill Nvidia updates their Optimus technology, people like me are stuck. Fortunately the second link provides a temporary solution. Simply moving (do NOT delete it, in case you run into problems), the d3d9.dll file to an other, not Skyrim-related folder made the launcher recognize my dedicated gaming card, and since then I've been able to run the game smoothly.

The caveat suggested by the second thread linked below is that you will not be able to run mods. In my case however, I could run mods fine. Which mods you cannot run specifically are the ones that depend on the d3d9 file (most notably, FXAA injector and the ENB series). Skyrim itself however, has proven to be able to run WITHOUT this file. And any other mods are working fine.

So there you have it. I really hope this is a temporary solution, because it's certainly not fair that certain people who bought Skyrim cannot enjoy all mods and graphical enhancers. I made this thread in the official forums so that other people may find it (I haven't found a direct thread offering a solution) and get their problem solved. Hopefully Nvidia will update Optimus soon.

Silverhammer

Sources

http://forums.nexusmods.com/index.php?/topic/512754-fxaa-injector-issues-major-lag-caused-by-d3d9dll-file/page__p__4186397
http://forums.nvidia.com/index.php?showtopic=216243