Someone who improved as an adult has written a book about how he achieved his improvement, so his experience must be very useful to you. He explains his training methods and helps you by saying how to do the same. I found his book on 3 websites, click if you want to see it here , here or read some pages here.
According to what he says inside you need a good book for tactics like this.
I saw a copy of "The Idiot's Guide to Chess" while out shopping with my wife one day, and bought it on a whim. I seem to recall it getting bad reviews from the hardcore chess people about being too this or not enough that, but it certainly did the job in my case. It gave me a much more solid foundation than merely moving the pieces and jumping at checkmates that were only checkmates in my imagination.
You could probably accomplish much of the same thing by working through all the Chess Mentor lessons from the bottom up. I've worked through a ton of Chess Mentor lessons, and it has really helped improve my game. I'm a cheapskate and not a big fan of spending money on anything, so it says a lot that I've renewed more than once.
Just play against Stockfish and try to understand opponent's moves. This is the best way (especially the best free way), but you must be calm losing 
Chess .com good way to practice and improve.
buy a chess set
Has Deviance posted in this thread since 2007?
Hasn't logged in since this post. Probably lost all his money buying his friends drinks.
It's a golden age for adults who want to learn chess.
The Idiots/Dummies books are perfectly fine for starting up. Many other books and chess sites as well.
After that, it's just a matter of how motivated you are.
I never had the opportunity to really learn chess growing up. I understand how all the pieces move, but I don't know any strategy. A friend of mine and I made a gentleman's wager to learn chess together. At the beginning of a night out, whoever wins a game of chess has to buy drinks for the night. So now the game is on!
Could anyone please recommend books, web sites, strategies, exercises, etc. that would help me learn this game quickly? I'm a beginner, but obviously not a child. Thanks so much for your help!
Maybe keeping away from the drinks and just focusing on the game?
But above all, you have to REALLY like playing chess...
I believe jiuchessu is onto something here.
I recently re-learned chess; I probably started not much better than you. I knew how the pieces move, but didn't know about any fancy moves like pawn promotion (thought you had to pick from lost pieces) and didn't know castling (thought it was an illegal move).
After reading Chess for Dummies (well, I was able to get thru 1/3 of it), I know the fancy moves but still can't play a decent game. What I find that helped the most was actually a chess video game called Majestic chess.
For example, it teaches you about pins, then sets you up against the computer where the computer is programmed to give you opportunities to use pins. It also goes thru many checkmate patterns where you have to recognize them within a short time limit; after a while, you kind of memorized them. And after playing 100 games where you must use back-rank checkmate against the computer, you're just trained to naturally look for them in real games.
Majestic Chess won't take you further than beginner stage, but it seems to have gotten me there relatively quickly (in 1.5 months spending about 2-3 hrs /week). I cheated and used the Internet to solve all its chess puzzles like placing the maximum # of knights, etc. which I don't think helps the chess game.
Good luck. Hope you win the bet.
Heck, just join a local chess club, if there is one near you, they will help you
Play a lot of games and Save those games . And if after some time , Give them to your coach , He will do the rest of the things 
Has Deviance posted in this thread since 2007?
do you think he learned how to play chess
For online chess coaching https://www.youtube.com/watch?v=a7HDBXCGDhk&t=21s
chess set
I am a hobbyist player with years of experience. I am 30 years old and I have FIDE Master Title and National Master Title (with elo about 2300). I've never had a coach, I learned myself - with selected books, online forums, analysis and practical games.
After years of experimentation and failure, however, I recommend investing in a good coach. I managed to win a couple of tournaments, draw with world champion in simultaneous tournament, but I lost a lot of time. The coach will say - do this, this and this. Results will follow, without worrying about something is right or wrong.
Why a good coach? Good, experienced coach can bring players to the high results. On Internet forums or in real life, you can get different opinions - not necessarily good.
BTW: When I started playing a was at the and of the table many times (below players at my age), so in my opinion I have no talent. So don't worry.