There are thousands of web pages devoted to the Vikings and related topics. Many of them have beguiling graphics, an entertaining style, and vast amounts of data. I'm not going to repeat, or compete with, all of that fine work.
What I will do is make some comments and suggestions, and provide some links. Use your browser and follow your interests. Eventually you may want to join one of the Viking groups and experience a portion of their lifestyle for yourself.
If you are interested in the Vikings, you'll want to read some of the Sagas and the Havamal. The Sagas are tales of the lives, loves, battles and feuds of real people in the Viking period. Many of them are available free on the net. One of the most famous, and best, is the Saga of Burnt Njal. Another is the story of the trollish warrior-poet Egil Skaligrimsson. . For laconic drama, there's always Heimskringla, the story of the kings of Norway. You can also download many of the other Norse Sagas from Project Gutenberg.
If you are a lover of fine books, and have a bit of cash on hand, you might want to look at The Complete Sagas of the Icelanders, edited by Višar Hreinsson. This is the complete and definative body of Viking Literature in new translations. It's not inexpensive, but if you like real books rather than downloaded text files you might consider it. I'd read some of the cheap or free versions first however.
The Havamal contains advice the "High One", Odin himself, on how to get along in life.
The mention of runes evokes ideas of symbols of power and mystery from Tolkin's stories, and similar tales. Tolkin was a medieval scholar, and took his inspiration from the actual beliefs and mythology of the period. For the Vikings, the runes were steeped in power and mystery, as befits their mythical origin, Oden himself.
The runes were a writing system used in Northern Europe. They were usually carved into wood or stone, so they consist of mostly straight lines. There were several variations in different places and times. The older set, or Elder Futhark, consists of twenty-four letters. The Scandinavian folks gradually simplified the futhark (named after the first letters) to the sixteen runes in use by Viking times. The Anglo-Saxons on the other hand, expanded the system to accommodate new sounds in their language.
The runes differed from our current alphabet in that each character had three levels of meanings. The first was the sound the letter represented, just as we do today. Secondly, each stood for a common word in the language that was its name. It's as if we named our letters "apple, boy, cat, dog", etc., rather than "aye, bee, cee, dee"..etc. The letter could be used for the word that was used as its name, much as we sometimes write "I C U" for "I see you". These two sets of correspondences are fairly well documented and straightforward. The third level is open to more interpretation. The Vikings were very fond of "kennings" or allusions. These were often convoluted and obscure. There was a set of associations around each of the names of the runes. Some of these were presented in the Runic Poems. These were a set of verses used to memorize the runes, their order, names and meanings.
These associations were almost certainly used for magical purposes, including fortune telling (rune casting). It's quite difficult to find good information on this. Most people who write about the "meanings" of the runes use more imagination than scholarship. Most reputable scholars avoid the topic. The majority of current writing on the use of runes for magical purposes is done by people who are interested in continuing this practice. They usually have knowledge of other magical systems, and this affects their interpretation of runic practices. They are often quite willing to fill in the gaps, or reinterpret available information to fit their preconceptions. At worst, they simply make up whatever they think will sell the most books and new age rune casting sets. Any set that contains a "blank rune" is modern rather than traditional.
Like writing systems, magical systems evolve and change over time. "New Age" rune casting may be an interesting study in itself, But it won't tell you much about the way the Vikings did it. If you're interested in the actual practices in the Viking times, you should go the primary sources as much as possible.
Besides the surviving inscriptions themselves, primary sources include the Runic Poems, the Havamal, the Sagas, and some incidental remarks by contemporary writers. The Sagas are probably the most interesting to read. They are great stories, and can give considerable insight into the culture, beliefs, and practices of the time. It's good to remember however, that most were first written down some two hundred years after the events they record. This was some eight or ten generations after the culture became officially Christian, although some heathen practices continued down to modern times.
There are some really good web pages on the Runes. The Omniglot site provides a good basic introduction to most of the writing systems in the world, including runes. The Runesmith has the most comprehensive page I've seen. Arild Hauge's Homepage has the best history of the development of the runes and their different versions, as well as some excellent discussion of early Viking culture. There are many more runic pages also.
Vikings were all pagans, right?
Wrong, many were Christian. Some say the most vicious were Christian. But
when folks speak of the Viking's religion, they usually mean the Pagan or Heathen
beliefs. These beliefs shaped their culture and helped make them the people we
find so interesting.
"Moreover, the faith which they practiced was no superficial one. It lasted well over a thousand years in the North, and has in it not a little wisdom. It developed out of the thought and aspirations of men born into a tough world and reared in a hard climate. They had learned to adapt themselves to life, and for the most part undoubtedly found it good, steeling themselves to face its blows when they came without flinching, and to waste no time in vain regrets. Thus for all our sophistication, we may indeed have something to learn from Scandinavian mythology." -H.R.E. Davidson in 'Viking and Norse Mythology'
The Heathen Viking Religion is a wide and interesting topic, with significance even today.