This is fairly easy to do, but takes a little time. All you need is some beans or seeds and a large container to do the business in. Smaller beans work best - Mung or aduki beans for example, but most kinds of legumes will sprout. Lentils will sprout if you use green or brown ones, but not the split variety. As for seeds, you can use shelled sunflower seeds, broccoli, mustard or alfalfa seeds and a whole bunch of others. Many seeds - especially the brassicas - make spicy, tangy sprouts; sprouted chickpeas are very tasty and fenugreek seeds retain a mild curry taste which is nice in salads. Experiment to find out what you like most. Here, I'll describe how to deal with a handful or so of mung beans. It's a similar process for all seeds - just the quantities and sprouting time might need adjusting.
One cup of beans will produce about two litres of sprouts, so make sure you have a big enough container. One with a wide opening is best otherwise it is difficult to get the sprouts out. Put the beans in the container and rinse with several changes of water, then put in enough water to cover the beans by about five centimetres. Leave the beans to soak overnight. The next morning rinse the beans with fresh water and drain all the water off. Cover the container loosely so that the beans don't dry out but a little air is allowed to circulate. It is important to rinse the beans every day to keep them fresh and to drain all the water off so the sprouts don't rot. At lest once a day is necessary, but two or three times a day is even better. I usually use a large jar and after filling with fresh water, I use my hand as a strainer and gently turn the jar upside down. That seems to do the trick (though this will be difficult with very small seeds).
Keep the container in a place away from cold draughts and if it's a clear glass container, away from bright light. If you rinse and drain the beans every day, after five or six days, you'll have a big pile of bean sprouts. Be more and more careful with your rinsing as the beans grow so the sprouts don't break. The skins will come off the beans as the sprouts get larger and if you fill the container with water, the skins will float and a lot of them can be poured away with the water. It helps to give the sprouts a gentle stir with the handle of a wooden spoon after you have added the water. This loosens the skins and separates the sprouts so they don't all grow together in a tangled mass.
When the sprouts are of a size you like, rinse and drain them one last time and put them in a plastic bag. They will keep in the refrigerator for a week or perhaps more.