You cannot increase the actual resolution of an existing image. There is fixed amount of information in the image, and when you increase the pixel dimensions (resize up) you're just spreading that information out and not actually increasing resolution.
Having said that, there are ways fake increased resolution. One technique I've used is to
- increase the pixel size slightly, maybe 10% or so
- then sharpen ever so slightly (an amount of sharpening on the verge of not being noticeable).
Repeat these steps over and over. You might be able to increase the size of the image and have it still look decent, but you might not, it depends on the image and it depends on the units of enlarging and sharpening. It might begin to look oversharpened, in which case you should start over and use smaller amounts of sharpening at every step.
There's also software that uses some high-tech magic to fake increased resolution, like Alien Skin Blow Up.