The method actually depends on what kind of jewelry your are trying to clean.
As an alternate to doing it at home, if the piece is basically metallic with gemstones, you can often just bring it to a reputable jeweler at your local shopping mall. They will gladly clean the item while you shop the mall, then pick it up when you return. They will usually place it in an ultrasonic bath, then steam-clean it and dry it when you return. They do this free because they hope you will consider them the next time you need to make a jewelry purchase. Be sure to ask if it is free though, because some do charge for this service.
If your piece of jewelry is more delicate, you have to take more care. Necklaces with silk or fibrous cords can not be subjected to harsh cleaners, and should be treated with care. Also, some gemstones are coated with a very fine oil that enhances the gem's beauty. Many cleaning techniques will remove this oil, and unless you replace the oil, your gemstone will appear dull and possibly worse than it did when you started. If you have expensive jewelry, you are advised to do some basic research on the cleaning methods for your exact gemstone (semi-precious or not).
If you have taken the above into consideration and still wish to clean your own jewelry, the easiest and safest method is to use simple dish-soap and a toothbrush. NEVER use toothpaste! Toothpaste has an abrasive compound in it that can actually scratch metals, and leave swirl-marks from your cleaning attempt! After brushing your jewelry piece with soap and toothbrush, rinse it well, then dry it completely. If the jewelry piece has a fibrous or silk rope holding it together, resist the temptation to immediately wear the jewelry. The cord will have absorbed water, and the weight of the piece (or the slight tension you may unknowingly place on it) will stretch the cord. When it dries it will then have spaces between your gemstones or pearls, which is not an attractive look, and there is no way to repair the damage.
Simple silver and gold jewelry can also be cleaned with special cleaning cloths, available at most jewelry stores. They can also sell you special cleaning products for hard-to-remove stains, or hard-to-clean specialty pieces