Can anyone recommend any good sources such as periodicals, websites, or what not to stay up to date on the latest opening theory? I am willing to pay if the source requires such. How do the top Grandmasters stay up to date on the latest theory?
The top players in the world keep up with theory by actually looking at the latest games to be played. Every week, Mark Crowther collects all available games and prepares them in downloadable format here: http://www.theweekinchess.com/.
For players who can't look at a new move and instantly tell the ideas behind it (pretty much everyone below FIDE 2600), there is the Chess Informant: http://www.chessinformant.rs/. It comes out 4 times a year and has been in publication since 1966. It won't keep you nearly as current as checking the TWIC games every week but it will at least have someone to explain the moves to you.
Another high quality source of opening analysis is the New in Chess Yearbook series. It also appears four times a year with hundreds of pages on the newest opening theory.
As already said, top GM keep up with the theory by simply looking at the games played. In think the sources provided by @Cleveland are excellent, and just in case you may want to keep up to the games live, the chess website ChessBomb follows the main events being played on the planet.
Another source for top opening preparation could be the "Master's Bulletin". This is a monthly magazine issued by the website Chess.com, featuring top GMs explaining their ideas and modern repertoires. It covers other areas of chess, but the opening is certainly the more treated. You may find the different issues here and the full list here. In that last link, some of the first issues are free, check them out and see if they meet your expectations on top preparation.
For tournament play, I find the useful website 365chess.com more than enough. You only need to get registered to benefit from around 3M games (the Big Database), organised by the popularity of the move made. This is not the latest theory though, as some relatively old lines are now out of favour at the top, but still have more played games in total than the modern ones. For the latest theory, you may want to become a supporter of the site (only one time is enough for full access) and get access to the Masters Database, where only games with both players over 2400 are included (and most are not included on the other).
The same idea as the Masters Database can be found on the webpage Chessgames.com. By being a registered member (which is free) you have access to a depth of around 12 moves, and have to become premium for the full depth. On this website you can also access the "Chess Games Collection" tab and look for a certain opening.
Update: ChessBomb has now been bought by Chess.com. It will be missed. Chess.com has also discontinued the "Master's Bulletin". It will be missed.
There is a paid journal at http://www.chesspublishing.com/content/ with different specialists monitoring different openings (this is sometimes referred in bibliography of chess books).
Chess evolution also has GM analysis: http://chess-evolution.com/
For game collections, also ChessOk, delivers small chunks free every month: http://chessok.com/?page_id=694
Also the GM Repertoire from Quality Chess, has many original analysis: http://www.qualitychess.co.uk/
Now, Since I am far from GM, I would also recommend as useful the Move by Move, Starting opening x series, and others from Everymanchess, http://www.everymanchess.com/
Chessable is a great website for opening theory for both beginners and experienced players. Various masters create new and fresh opening courses which might not have been analyzed deeply before. It has free and paid courses, and paid courses are usually really big and comprehensive. Some paid courses also has free demo versions which allows you to see the opening choices of the author and decide if you want to learn more deeply about it. (I said courses but they are like interactive books.)
The website tries helping you to learn by offering a system where you need to repeat your studies daily/weekly. It is similar to Woodpecker method if you are familiar to it. However, you do not have to do these repetitions like me and use the site as if it is a library and you can check openings from time to time whenever you need them.