I have been sprouting for a while now and originally started sprouting using the "traditional" method of seeds in a cloth, etc. Anyway, since then I have graduated :-) and believe that using a device called the Sproutamo is perhaps the easiest and most efficient method I know of. The device is reasonably cheap (I have three!). The device is made of food grade plastic and using it is simplicity itself. It essentially consists of two vessels: one outer vessel (lets call it the shell) and an inner vessel with slits in the bottom (lets call it the container). Essentially, the shell houses the container that in turn houses the sprouts. The device also has a couple of covers: one that you use while sprouting (it has slits) and one that you use to cover and store after you are done. I could not believe how much less time I spent growing sprouts instead time spent cleaning out the sprouting cloth (in the traditional method).

Anyway, the steps I use to grow sprouts using the Sproutamo are as follows:

1. Select your seeds of choice. Possible choices to start are mung beans or dried peas. Try organic ones since I have found these tend to have less of those very-hard, impossible-to-soak, break-your-teeth, duds in them. Use an amount that fills about a 1/3 of the Sproutamo (these things can really grow big).
2. Wash and soak in plenty of water for 12 hours. Wash using the Sproutamo itself by filling the container with seeds and draining with cool tap water.
3. After the 12 hour period drain all the water thoroughly (truth be told the instructions with the Sproutamo suggest a method of draining that I completely skip, I simply just shake it several times) and place the container in the shell in such a way that will allow for air flow (diagrammed instructions with the Sproutamo show how this is done).
4. Depending on how warm it is you will start seeing sprouts within 12 hours. You can let it sprout more if you like long sprouts or simply start munching as soon as you see little sprouts. AFAIK, nutritionally it does not matter but flavor changes with time. I like my sprouts long so will generally let them grow a couple of days longer. Note: it is also suggested that you rinse and drain every 12 hours. I started doing this but now I skip this step too!
5. Refrigerate sprouts that you do not eat immediately. They will keep for several days.

A point of note regarding mung beans: if you like your mung beans to have really long sprouts then place a weight on them when sprouting (don't ask how this works---it works!). I simply take a 28/32 oz yogurt container filled with water and place it right on top of the sprouting mungs in the Sproutamo instead of the lid.

Finally, a one stop shop and resource for sprouts is the Sprout People

Disclaimer: I have nothing to do with the Sproutamo except that I am very satisfied user.