How would I go about making my webcam shots look less… gritty? I have pictures, and the quality suck. Is there any way I can tinker with the webcam to help that?
No.
Your webcam is equipped with a sensor, the better the sensor can detect wavelengths of light, the better quality the image. Unless you buy a new sensor…no.
How much would one (good) sensor cost?
As much as a new camera. Though the sensor is pretty much the entire camera, the rest of the camera is designed around the sensor, meaning you cannot just swap a new sensor in. To buy a new sensor, you’ll need to buy a new camera 
3.0 MegaPixel cameras are relatively cheap, around 100 bucks (USD), and generate images that you would define as photo realistic. Anything below 3.0MP will not look realistic, and anything above is (generally) overkill.
Though, if you want a WEBcam, something to transmit live moving images to other people, then i have no idea. Due to the nature of a webcam, i can imagine that the image quality will always be shitty. This is because the sensor needs to be able to take images fast, to create the guise of “live footage” rather than take one or two nice pictures every minute like a camera.
And while we are on the topic of sensors, i’ll flex my nerd muscle here and go into a little detail. Each camera comes with something called a CCD. CCD stands for Charged coupled device, if memory serves. It is made up of thousands of phototransistors. These transistors detect the intensity (and hence, frequency, and hence, color) of a certain section of the lens. Each of these working in unison provides an image of a part of the lens, and combines it into a larger area, called a pixel. Each of these pixels is then combined into Megapixels. You see on the screen the result of each transistor’s capture of light.
Some cameras even implement multiple CCDs, the most famous of which is Sony’s “3CCD” system, where there are (duh :P) 3 CCDs, however, each one of them captures an image of the entire lens, but at different frequencies. So maybe one CCD captures red, another green, and the final blue. Then, all three are combined to make one image. This provides MUCH better color and image quality, since work is spread between 3 items, and each item only needs to sense a smaller area.
And you know those new camera phones? There is no way a CCD could fit in one of those, and retain high image quality. A new method of taking color and changing it to data has been invented, and is called CMOS. Though CMOS is NOTHING new, and has been around since the 60’s, its application in imaging is new. It is coated with a different material, and uses less power.
So yea.
You rock. D:
I don’t really need it for live video streaming; I just need it to take good quality stills from my computer.