How do I hook up my PS3 to both surround sound and my television with the one hdmi slot?

May be...

simple, use the hdmi to the TV, then use a set of RCA cables [red, yellow and white cables] (like $10 @ radioshack) to hook the TV Output to the surround sound input. Most VCR or DVD players have them in case you don't have a set laying around.

You could do it as above or it might be possible to get an hmdi splitter that has 1 hdmi cable going into the splitter and then 2 to go out and one goes to tv and the other to sound system or use the hdmi for tv and the AV for surround sound. You just select the output for you ps3 video through hdmi and the sound through AV. or find a reciever that has input output for hdmi and run one hdmi into receiver and 2 out one for tv and other for surround sound. That the only thing I can think of other then the way above

easiest way is to go through a receiver that has hdmi then go hdmi out to tv

hdmi tv -ps3 has your speakers got optical for ps3