There are three courier missions in all, one in each major city. These don't show up on your map, and indeed aren't visible from the street; in order to discover them, you'll have to hop onto a bike or motorcycle outside a business, at which point the mission will automatically begin.
Los Santos: You can find this mission at Roboi's Food Mart in the Commerce district. There's a BMX bike outside, jump on to get going. San Fierro: Located on a Freeway motorcycle outside a Hippy Shopper in Queens. There may be more than one of these shops in Queens, so look around for the bike. Las Venturas: Get on the Faggio outside of Burger Shot in Redsands East.
In the courier missions, you'll have to ride around and deliver a number of packages within a set time limit. You deliver the packages by locating coronas set alongside certain streets; when you're next to one, do a drive-by (L2 or R2 buttons, O button to throw) to chuck one of your packages through the corona before moving on to the next. You can't be moving too fast when you do this, though, or you'll miss the corona; if you do, you can return and pick up the package and try again, or just throw out another package. If you miss a package and throw another one before picking up the first, the first will disappear, but you should have a few extras on each run. Extra packages are converted into cash between each level, though, so if you're strapped for cash, you might want to throw as few packages as possible and save the rest.
Beyond that, the game is fairly simple; throw packages through a certain number of coronas in a certain amount of time, then return to the shop before your time limit runs out. Timewise, you should be fine so long as you choose a correct route. All of the coronas will appear on your map at the beginning of a round, so open it up and try to get an idea of a good path to take. Each round will have more coronas, but will also extend your time limit, so as long as you're familiar with a city, you shouldn't have too many problems. You will have to use the same vehicle for all four rounds of a specific mission, though, so you may have to duck into a Pay N Spray if it starts to smoke. After four rounds are up, you'll get cash for the last round, and will gain the store as a business asset.