Look, you can add more pixels to your image but it won't increase the resolution. The native resolution of the image is based on your sensor or film, not what do you with it in Photoshop.
There's a decent explanation of PS' resampling methods here. They each have different applications. They will alter the way it resizes or resamples, but not really the resolution.
If you want better resolution, you need a bigger or better sensor or film.
Okay, to summarize from a different person's point of view ...
The image you took is the maximum resolution you're going to be able to get - each pixel has a piece of the information for the image. There are various programs that can re-sample the image, effectively changing the number of pixels.
If you down-sample - decrease the number of pixels - then you're usually going to get a somewhat "better" image due to lens distortions, sensor noise, and other things that come into play and make it so that each original pixel doesn't necessarily have a unique piece of information.
If you up-sample the image - increase the number of pixels, you're not actually increasing the information in the image, you're just increasing the number of pixels that information is spread over. Like if you double the image size, then 1 pixel is effectively "spread out" over 4 pixels (2 width by 2 height).
Now, there are different algorithms for up- and down-sampling images, and some are better at certain things than others. Alpha gave you a link that explains how Photoshop's algorithms work (I assume ... I haven't actually looked). Usually, they're fairly good at giving you a smooth enlargement. However, the key thing to remember is that no interpolation algorithm can give you more information than you had in the original image, it just spreads it out.