Well, the real answer is that you can’t really. When you make a picture bigger the computer has to make new pixels- this is called interpolation. However, there are ways in which you can enlarge pictures somewhat without losing too much quality. You can use the image size dialogue box and increase in increments, or there are plugins such as Genuine Fractals which do the same sort of thing. People have had very good results with Genuine Fractals, that should be worth you checking out.
For a quick and dirty method, try upsizing the image in several steps of 110% and see if it’s acceptable. i.e. Step A = original image x 110%, Step B = Step A x 110% and so on.
Note: the key, according to Scott Kelby, is a 10% incremental upsize with each step with the Resample Image box checked in the Image Size dialogue.