Runes are simply old Norse/Germanic alphabets. There are actually a bunch of different Runic alphabets. For example Scandanavian Runes used by people from Norway and Sweeden. Gothic Runes were used by early Germans. There are Anglo-Saxon Runes. As well as just anglo or Saxon Runes. There are Danish Runes. Then there is the Elder and Younger Futhark Runes. Which are most popularly used in modern day Runecraft (divination and magick through runes).
Personally I have always prefered to work with the elder futhark Runes:
http://www.omniglot.com/writing/runic.htm (along with a few other variations too)
The only rune not shown on that site is Odin (unknowable). On rune stones it is the one with no marking on it at all.
Runecraft itself can be used in a variety of ways. They can be used for divination through spreads similar to those of Tarot cards. Or one may contemplate an issue that is bothering them in life (something serious, not "Does Susi like me?") then draw a stone from a bag and meditate on its meaning in relation to their question. Apart from divination Runes can be used as part of spell craft. Each Rune corresponds to natural forces and elements and mythical beings. Simply wearing a particular Rune can enchant a person and infuse them with the Rune's power. So for example if you want to have more strength you could wear the Rune Uruz. Or if you wanted to be victorious in battle you could wear Teiwaz. Through more advanced magick you can create seals or write spells using Runes. You can carve Runes into candles for candle magick or paint them on cords for cord magick.
Basically Runecraft is an art that uses Runes as a tool to accomplish virtually any magick feat. Runes are just one of many different esoteric alphabets used in the Occult.
You can also make your own runes. If you live near a lake or river go find yourself some flat, smooth stones and paint or carve the Runes into them. Using something like a leather or wool bag you can place the stones in that bag and you're pretty much set. You have your own Rune stones that you can use for magickal purposes. Or you can to any occult store and most book stores like Boarders or Barns and Noble and buy a set there. With that you'll also most likely get a book that tells you about Runes, some of the history, ways to use them and what the Runes actually symbolize. But if you make your own Runes you can just look up their meaning online. If you get into Runecraft I suggest you make your own because truly effective Rune magick requires that you have a strong personal connection to the stones you are using. By making them yourself, you put a part of yourself into them. However, you also do that if you just use the same set a lot of times.
Personally I have always prefered Runes over the Tarot, though both are useful and its nice to use one or the other as a sort of "second opinion" when using divination.
If you like Runes you might check out I-Ching (pronounced EE-JEEING)