Ratings help you find opponents who are similar in strength. When you seek a game, you can set it up so that only players in a certain range can accept the seek. Most good sites (definitely this one too) have enough players that >90% of us won't have a problem finding a challenging game.
Fritz12 will be great for pointing out moves you wouldn't have seen on your own, and perhaps with it's built in opening book to point out lines you may not have known were there, but the program itself will have little to do with your improvement. BTW Opening "book" or opening "lines" are established and respected (read strong) sequences of opening a game.
Well, I suppose you could load positions that are winning for your side, and test your winning technique by playing against the computer. This is where chess strength comes from, through the effort of pushing yourself to find good moves again and again. Also because you know the computer wont fall for a trap it forces you to be more objective in deciding how your opponent might respond.
More specifically, it just depends on your current level. Many (if not everyone!) will tell you tactics are important (solve tactical puzzles) and that's true (e.g. tactics trainer). You should also know the basic over-kill mates (king vs queen, K vs R+R, K vs R), the basics of opening a game (the center, develop, castle, and the like) and the basics of strategic play (backward pawns, doubled pawns, pawn majorities... a lot about pawns actually 
).
After that improvement has a lot to do with more playing experience (play a lot of games!), and how objective you can be with your move selection... meaning don't give away pieces for nothing, and don't assume your opponent will fall for tricks. Try to love your move for itself, not because how you think your opponent might respond to it... nearly impossible advice to follow when you're new to the game, but as you learn and keep playing it's important to know this is what you're shooting for.
Hi,
I am new to the site. I was once an avid player, and have developed a new passion to re-learn chess at an elevated level, hopefully progressing beyond beginner over the next handful of years.
How does one find opponents of somewhat equivalanet ability? And are their mentors available?
I ordered the Fritz Twelve, it arrived yesterday, but I hve not had time to explore it yet.
Any comments or suggestions are welcome.
Thanks,
Dan