Aditionally, you can assign and unassign people based on timed promotions.  Or, you can have all your customers (or a select few) assigned to a given price group, we'll call it "weekly", and each week you can change the products assigned to this price group which will in effect create weekly specials for your customers. 

If you use this method it is helpful to create a category called "Weekly Specials" and assign the same products to it that are assigned to the price group.  While this category will not in itself provide the customers with the price discount, it is useful in letting customers know what is on sale that week.  Of course you can also use this method on a daily basis and call it "Today's Specials" if you like.

If your store sells books, toys, gifts, and flowers, you may want some customers to recieve the wholesale price on books and toys but only a 10% discount on gifts and flowers.  You can accomplish this by creating two price groups, one called "Wholesale" and the other called "10% Discount".   There are two ways to proceed from there, which one you choose depends on how you have your price groups configured. 

If the price overlap is set to give the customer the lowest price, then you assign all the products to the "10% Discount" group and only the books and toys to "Wholesale".  Now assign the customer to both groups.   If you have some customers who are only entitled to a 10% discount, simply do not assign them to the "Wholesale" price group. 

If you have configured the settings to charge the customer the highest price in the case of an overlap, assign all items to "Wholesale" and only the gifts and flowers to the "10% Discount" group.  Then assign the customer to both groups.  For customers that are entitled to the wholesale price on everything, simply do not assign them to the "10% Discount" group.