What is the best way for a newbie to become more in tune with the use of Runes?

As another newbie, I may not be qualified to answer this, but I can at least share my experiences.  I bought the book "A Practical Guide to the Runes" by Lisa Peschel.  A low cost, easily read treatise that even mainstream bookstores like Barnes & Noble carries.  Rune Rede and other more sophisticated texts will wait until I have a better idea of what I am doing.  I have posted a few entries on my blog about my first runecasts, so you might find them helpful (or amusing, or whatever.  Blog is here:  http://www.mysticboard.com/weblog.php?w=78).

The internet has a lot of information, of course, but a small book like the Peschel text might be a good place to start.  It distills the information into something usable; you don't have to sift through hundreds of web pages.  Although there are some good sites out there that can get you started.  I would go with the book and then use the internet and intermediate/advanced texts to move beyond basic knowledge.  At least that's my plan.

Since we are all unique, there is no best way for everyone. The important thing is to make the runes a part of your basic consciousness. My teacher years ago used a combination of guided meditations on each rune and a study of traditional uses and meanings. Recently Diana Paxson wrote a book called "Taking up the Runes" which uses a similar approach. I would recommend it highly.
Choosing a different rune each day and meditating on it's meaning and looking for it's operation in everyday life is another good method. After many years of working with runes, I still use this and I am still surprised by what I sometimes find.

Every book I have seen suggests the daily meditation on each rune.  I have to admit I have been... well, not skeptical, but unconvinced.  I always thought that it wouldn't help.  Not that I am an expert, to disagree with people like Ms. Paxson, but I guess I don't always have that opportunity for quiet meditation.  But, having said that, I like referring to the texts I have and handling the runes from time to time, so while it is not a formal meditation, it is a spontaneous bonding (if that is the right word) that might do the same thing.  While I suspect that the meditation is superior, for those who just can't stop everything and need a quick pit stop with the runes, this may be a workable solution.

Additional advice is to dive in.  The runes will not bite back.  Approach them humbly, reverently, lovingly, trusting in Odin (or Freya, if you think like me), ask for their assistance, and let them do the rest.  Of course, you still want to educate yourself on their use and meaning, but I found myself unable to not dive in, Freya be praised!

Hi just thought I would put my two cents in, hoping to be helpful.  I started my Rune Journey years ago, starting off with a Teacher which did not work out so well as you have to trust your teacher.  So my road became solitary and I absorbed any books I could get my hands on about Rune reading.  I started off with Rune Magic the history and practice of Ancient Runic Traditions by Nigel Pennick which suited me fine.  I read lots of other books which did not make much sense to me and some time conflicted with the meanings of each rune.

Before I got stuck into the books as impatient as I was back then I went to a "New age shop", and purchased my first set of Runes.  Which came in a box with a book with it, the meanings of the runes were so way off which made me go to look at other books for help.

It does help to meditate over each rune, but if you don't have the time for meditation.  Just keep on delving into that bag and pull out a rune and study the meaning eventually it will come to you and you will get the feel for the runes.  Not just the knowledge of what they mean but the feel for them.

Good Luck on your journey!