With the category discount function you can add a discount to be valid for all the products in the category. More information about how on this page.
It is possible to sell the same product for different prices to different customers. This page has instructions on how.
Discounts for the products in your shop can be set in several different ways. All the functions are not available in all the shop levels. In these instructions you can read more about how to set up the discounts and what is available in the different shop levels.