It is correct that this GPS unit should be able to plug directly into your PC without extra power or regulator devices. When using an FTDI chip, you are correct in using a MAX232 driver. The issue here is, your GPS may have damaged the FTDI by sending signals at 12v TTL.
First, hook it back up to your Arduino, and make sure it works there. After verifying function there, you should indeed re-interface the FTDI with the MAX232. A free membership at Digchip.Com will get you access to this datasheet; http://www.digchip.com/members/part_details.php?s_id_member=112484183700162941776&id=3064316 Page 23 details general hookup for a MAX232 to the FTDI chip used in most Arduino platforms I've worked with.
Depending on your Arduino platform, the FTDI may operate at 5v or 3.3v, though the 5v series is far more common. Sometimes, some devices will simply refuse to talk to a USB serial converter, but typically a properly wired MAX232 interface will typically do it. Here's a schematic designed for a digital camera, but you can safely cut off the right half of it for your application;
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