Pushing is simply underexposure combined with some method of development intended to bring out whatever shadow detail was recorded (ie maximize film speed).
Originally Posted by pdeeh
The simple push method is to extend development time. The problem is this also increases contrast. So various techniques are attempts at maximizing shadow development while holding back highlight development somewhat. This is often referred to as "compensating" development. There are different ways of doing this, some more successful than others, and regardless of how many experts you hear from, compensating development is not very well understood. One procedure aimed at compensation is stand development or semi-stand development. The idea behind it is "controlled" local developer exhaustion taken to its extreme. Since there is little agitation, the developer is expected to exhaust in heavily exposed areas while it continues to work in areas of low exposure (shadows). What is not well understood is how important both the film emulsion and the developer formulation are in determining how much compensation you actually get. Often there is significantly less than expected (although people still see what they want to see). Further, compensation does not necessarily imply film speed is maximized. You need the right developer.
Also, while I won't beat the proverbial dead horse regarding the risks associated with stand development, I still think it is important to do proper testing for uniformity. Usually the examples people post (aside from being high in contrast with poor shadow detail) are fairly "busy" images in which uneven development might not be immediately visible. But as with any extreme development technique, tests with more uniform, featureless tonalities should be done to ensure you don't end up with unexpected problems at some point.