You develop the film for a longer period of time than normal. The increase in time depends on how many f stops the film was underexposed. The increase in time is sometimes expressed as a percent of the normal developing time rather than in minutes and seconds. The actual increase in minutes and seconds will depend on the developer and the temperature.
Instead of defining the underexposure in f stops, you can also define it interms of the ISO film rating. If the film is rated at ISO 100 and you underexposed it one f stop, that would be the same as rating it ISO 200. If underexposed two f stops, the ISO rating would be ISO 400. Each reduction of an f stop is the same as a doubling of the ISO number.
As noted above, push processing isn't a something-for-nothing situation. You gain the ability to get a usable negative with less exposure, but the negative will have increased grain and a reduced gray scale. Finally, it's all or nothing. Unless all of the exposures on the film were taken at the same ISO rating, some [those taken at the normal ISO rating] will be overdeveloped.
Push processing is something you resort to when normal exposure and processing will not do the job.