This build puts early pressure on the Zerg while still allowing for an expansion, though has a later Nexus than an FFE. It punishes a Hatch-first somewhat well and can hold its own against Pool-first. The Zealots can usually make themselves worth it. The Zerg usually won't be attacking you as your Nexus goes down as your first Zealot will be getting to his base by the time you throw the Nexus down. Your second Zealot shouldn't be too far behind, with the third Zealot not too far behind him -- try to keep these guys alive for as long as possible. 3 well-micro'd Zealots can take a lot of Zerglings on, just don't get surrounded ("stutter-stepping" the Zealots is a good way to avoid this). Generally I've had more success just attacking the expansion with the Zealots, but if you think you can do more damage in the main, go for it. I've normally had more success sending the Zealots right when they are built rather than waiting for all of them to build.
The reasoning behind both Gateways at 13 supply is A) It is more economic than 11 Gateway, 12 Gateway, and B) While it gets slightly later Zealots than 12/14, the 3 Zealots are closer together in build time, so you don't have as much risk losing one before the next arrives, allowing you (with a bit of micro) to send each Zealot right when it arrives. You also have a better economy than just cutting Probes for the Zealots, allowing for a faster Nexus.
After that, just use your discretion. If you'd rather have Probes a little earlier or want Zealots a nibble faster, adjust.
Use the 9-Pylon and two Gateways to start a wall at your Natural. Unless you're feeling particularly cheesy (in that case you might want to proxy a more aggressive and less economic 2-Gate instead, as it will get earlier Zealots). Later, you can use the Cyber Core to help wall.
In the case of a proxy Hatch, get more Zealots earlier if you need to, and/or Cyber Core and Assimilator (and/or Forge and Cannon[s]) before Nexus. Use discretion.
If you can use the 16-Pylon to block the Zerg's expansion, do it if you want, and use your Probe to scout for the expansion at a 3rd instead. Otherwise make it at your wall.
If you don't scout any expansion from the Zerg, use the Forge adaptation mentioned below.
If you have confidence you can kill the enemy's expansion, or completely kill him, feel free to make a couple more Zealots before you expand (or, if you think you can just win, you can just 2-Gate all-in with continuous Zealots and/or 4-Gate).
In the case of early Pool rushes, do not try to block the Zerg's expansion with your 16-Pylon. Double-power your Gateways so you don't have as high a risk of not getting your first Zealot out. Use Probes to help as necessary.
You choose what to do with the two Zealots made after the Nexus. If you have a large area to wall, you might want to use both to help wall. If you think you can do some more damage, you might send both to attack. Or, use one to wall and one to scout/harrass.
You can transition into pretty much anything you want from this build. 4-Gate Robo, 4-Gate Stargate, 6-Gate Robo/Stargate, 6-Gate Double Stargate, DTs, 7-Gate all-in, 8-Gate all-in -- just use discretion in what you transition into and when you take your 3rd, etc. Remember that you need Phoenixes against Mutas unless you're all-inning, though pressure can delay them. A Hallucinated Phoenix can usually get some good scouting info.
Note that I don't have the exact times down -- just do stuff as fast as you can. Also, make sure to make supply count adjustments for getting things faster (pretty sure mine gets things as fast supply-count as possible without skimping on Probes aside from getting the 2nd Gateways and making room for the 1st Zealot, but if you can do it faster, go for it) and for the cases of your scouting Probe and Zealots dying.