Once you have everything hooked up turn on the tv and set it to the HDMI port as the input to display. Now, turn on the PS3 and (if this is the first time being hooked up) the tv should adjust to at the very least 720p.
If you are seeing nothing and you are sure the tv is set correctly put the PS3 in standby and then hold the power button down until you hear several beeps- this will reset the PS3's output settings. You can doublecheck your settings for the PS3 in Display Settings in the Settings menu. Select HDMI and move right, then checkmark the correct boxes (if on a 1080p tv just check the 720p and 1080p boxes- most games run at 720p and your blu-ray will run at 1080p). Move to the right again to see a summary page. Hit X to save the settings.