If you want to experience this kind of AwakeningI've given some of my ideas and suggestions below.
  • Read Lord of the Rings to start with.  Remember it and keep it handy, maybe not on your desk, but certainly not buried in a box at the bottom of a pile of 6 other boxes.
  • Read anything else concerning Middle Earth that you can find.  The Silmarillion is invaluable for putting everything into historical perspective.  Maybe difficult reading for some but it is truly worthwhile if you want to understand how to behave as any of the races and know how rivalries and friendships formed.
  • Ensure you have an appropriate name .  Do not choose a quenyan (language of the High Elves) name for a dwarf or Hobbit.  There are a few places where you can get help choosing names.  The first one is the appendix to Lord of the Rings .  This has the genealogies of most 'people' in Middle Earth, you will find many of them already taken but it is a start. 
    Secondly, there are sites that have the etymology (listing and origin) of different words as Tolkien himself devised eg. www.geocities.com/athens/parthenon/2196  or     www.mume.iwarp.com.
    Thirdly, there is a name generator associated with this site and there are similar ones in other places on the internet but please dont ask me for addresses, I have no idea!
  • Understand that becoming who you are means you have to know who you are first.  Make a history or story behind your character and make this accurate for your race and sub-race.  That means you don't have a half-elf that has two elvish parents and neither would a dwarf have been brought up in Lothlorien, since the elves of that land have no trust for dwarves.
  • Roleplaying (the art of appearing as if you are your character living in the land of Middle Earth  as if it is reality.) is for enjoyment.  As Londriel so wisely pointed out to me "Respect each others roleplay and do not try to force another to roleplay the way you want. Roleplay only works if all participants play together, with each other rather than against each other."
  • Develop a personality the suits your race , your past and your goals for the future.  For example a dwarf that lost his kin in the mines of Moria and has vowed to avenge their blood should be courageous, possibly aggressive yet have a sort of distant sadness in their eyes.  You should take on an accent or word pronunciations that once again suits your race, etc.  A hobbit would seem to mutter to themselves a lot and be often 'befuddled' etc if you wish to take on Bilbo's example.  Likewise also if you take on a wise and noble elf an ol' English type speach may be appropriate, as seens when Galadriel speaks to Frodo.
    This would also include social actions.  It would not be uncommon to hear a dwarf curse or see them spit, but to see a high elf do such you may start to wonder just how noble they were.
  • If you decide to adopt your character and make them real keep in that frame of mind constantly. Stay 'In-Character'.  Use the comment or -- for 'Out-of-character' statements or information.
Hmmm... there are many more ideas and things to think about to truly 'live' in Middle Earth. I will endeavour to have a new idea for you regularly.  And if you have ideas let me know.