In this image,
the "Image Size..." dialog from photoshop:
Pixel Dimensions: are the number of actual pixels your image is made up of.
Document Size: is a completely relative sorting of the pixel dimensions. Examples below.
Scale Styles: toggles scaling of layer styles when resampling the image. There is an upper limit to the scaling for styles and no warning when it's exceeded (typically only an issue on very large or very high resolution images).
Constrain Proportions: automatically adjusts Y dimension when for a typed value of X.
Resample Image: Toggle on to allow a change in the Pixel Dimensions of the document.
Examples of document size. For the example, a 2400x3000 pixel image, the print size is 8x10 at 300 dpi (8"x300 dpi = 2400 pixels, 10"x300 dpi = 3000 pixels). The same pixel dimensions print 16x20 at 150 dpi. To get a 16x20" at 300 dpi, you would need to double the pixel dimensions to 4800x6000 pixels (16"x300 dpi = 4800 pixels, 20"x300 dpi = 6000 pixels).
Now, increasing the pixel dimensions via the image size dialog will probably NOT improve your PRINT quality
. Photoshop (and no other program) has to simply guess at what those extra pixels would be - a function also performed by most consumer and most commercial printers (and they do it in a manner specific to that printer, something photoshop can't). Don't believe me? Print it once at 96 dpi, then scale it up to 300 and print it again. It might even be slightly worse.
That's not to say there's nothing that can be done to improve your image, just that simply scaling it up will not help, by itself. Scale up, then sharpen/bump contrast/etc as appropriate to the image and you can end up improving the situation. However, chances are, if you're asking how to scale an image, you'll probably need help to do anything further.
There are also other products that use fractal scaling to resize images, but with plenty of experience with several of them, I can confidently say their results are inconsistent - sometimes they work great, sometimes not so much.