Contrary to popular opinion, pushing or pulling film does not change the "speed" of a film one iota. Pushing a film means to extend it's development. Pulling a film means to shorten development.
Exposure increases an image's density in both highlight and shadow areas roughly equally (actually it's a curve, this is what is referred to by the term "characteristic curve," the amount that the density of a film will increase as exposure is added). Changes in development, however, have a much more pronounced effect in the highlights. This allows one to change the overall contrast of a film, as the shadows pretty much stay put, but the highlights go up (in the case of pushing) or down (in the case of pulling). Some photographers, in a pinch, utilize pushing to compensate for a lack of exposure. This is really a last resort, because, as I said, the underexposed shadows will remain just that, underexposed. The mid-tones, as well, will be a bit thin and muddy. Only the highlights will truly exhibit proper exposure, and this comes at a cost, increased grain. One could also compensate for overexposure by pulling a film, at the cost of flattening contrast.
Ideally, pushing and pulling are contrast controls. Pros who use chrome films push and pull all the time in small amounts (say 1/3 of a stop) to control their contrast.
So, to re-iterate, "pushing" is an increase in development, which increases the density of highlights, thus increasing contrast, simultaneously increasing graininess, most especially in the highlights. "Pulling" is a decrease in development, which decreases the density of the highlights, thus decreasing both contrast and, to a certain extent, grain.
Finally, the rating of a film's speed is actually the rating of how much exposure is required for the film to begin to record density above its film base and fog, in other words, the density of the shadows. Changes in development have little impact on these shadows, so a film does not get any "faster" by pulling it. Just to get that straight.
Hope that answers your question. Some very basic knowledge of development is essential to a photographer.