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There are several options available in this general ballpark
1) Play by Post (PbP): This is a fairly slow but intense option, as you are basically using a dedicated forum thread to run/play your game. These usually take days or weeks to play out, and tend toward more RP than "live" games, as the time limits are vastly different.
2) Virtual Table Top (VTT): Due to improvements in computers and Internet service, these games usually use a set of programs to simulate the tabletop with maps on it, dice rolls, and a voice chat/conference call to allow regular discussion.
These typically run in about the same time frame as a face-to-face game these days, due to a mix f improved technologies, and the ability to prebuild commonly used dice rolls using macros. James Wygle, one of the VOs who has started playing online more often, has a short overview of some of the things that Roll20, one of the commonly used VTTs, can help to automate play.
For online play like this, it is recommended that you have a headset/microphone, especially in a public location, but as long as you can mute your input, you can get by without.
One advantage, in my opinion, of any of the online play options is that you get to play with people allover the world. I am running the Rise of the Runelords AP online, and my players include a young lady from Singapore, while I live in Las Vegas, Nevada.
I have also played or run games with people from almost all other parts of the world. That has also included playing and GMing several of the multi-table specials online.
For one of the more active groups for online PFS games: Pathfinder Society Online Collective.