Basically... You don't - at least not directly.
Pixels are an on-screen measurement and DPI is a print measurement. However, when you print an image, you can usually specify the print density. A 700x700 image printed at 300dpi will be four times as large when printed than at 600dpi. (Yes, four times... Two times width x two times height = 4 times.) 300 dpi used to be the common print density. Now it's getting to be 600dpi, depending on the printer and how old it is. Some printers default even higher now.
More info:
If you take a look at screen resolution specifications, you'll note that different monitors (LCD and CRT) have different dot pitch for the pixels. For example: a 17-inch monitor with resolution of 1280x1024 pixels will have a smaller dot pitch than a 17-inch monitor with resolution of 1024x768.
A wild guess: The client probably wants the specific size (700x700) to fit their web page dimensions, and to