You can clean the different parts of the toilet in any order you like, but, if you're in a hurry, you may find that it's smartest to start with the bowl. This way, if you splash any dirty water out of the bowl while you're cleaning it, it won't get parts of the toilet that you've already cleaned dirty. Use a toilet brush to scrub away any stains or mineral deposits you see. You may need to apply some pressure to eliminate caked-on stains. For added cleaning power, drop a little toilet cleaner or all-purpose cleaner into the water, then dip the brush in it.
Now that you've cleaned the bowl, it's time to clean the main points of contact - the top and bottom lids. Use all-purpose cleaner and rags/paper towels (or disposable sanitary wipes) to give both the lids a quick but thorough cleaning on both sides. If you want to, use an old toothbrush to scrub the hard-to-reach spots between the lid and the body of the toilet as well as the hinges.
Finally, it's time to give your toilet's porcelain a squeaky-clean shine. Using a spray bottle, mist the exterior of the toilet with an all-purpose cleaner. Use a rag or paper towel to wipe down the toilet's porcelain, paying special attention to the handle. Alternatively, you may simply dip a rag or paper towel in cleaning solution or warm water, re-dipping the rag or towel when it is soiled.