How can I build a LEGO marble pump?
A pump is one of the most classic GBC (Great Ball Contraption) modules but is indeed difficult to get right.

One of the best illustrations I know is on this site:



Unfortunately, most of the site is in German, but the pictures are usually illustrative enough and I think it's a good source of information for ball machines in general, not only LEGO ones. The best is of course to get in touch with one GBC builder at events and ask for information.
EDIT:

Here is a picture based on the model at aforementioned site: 

Here is a video showing the mechanism in action.