The HDMI cable will deliver Video & Audio to your tv to the input you plug it into. You will need to make sure the tv is on that input when you want to use the PS3. Obviously the power plugs in the wall.
You mentioned a receiver, how does that come into play? Are you using it to power a surround sound setup? Please describe.
I'll give you an idea of the what I do I run an hdmi from my PS3 to my Yamaha surround (in the input) and have another hdmi running from the surround (output) to the TV.
This requires 2 hdmi cables.
Alternatively (if you don't have a surround) you plug one end of the hdmi into the ps3 and the other end into the tv.
The input on your tv will likely be in the back with another on the side.
Pro-tip: don't turn on the ps3 until it's all plugged and you make sure that you're tv is on the input that your hdmi is plugged into (if you messed that up it may not auto-detect that you plugged it in to an hd tv in the case of this turn it on and wait for it to show a green and a blue light on the right side of the front, then hold down the I/O button till it beeps and then a bit longer after that)
The input on Playstations is the only annoying thing about them you'll enjoy it after this.
I plug my PS3 HDMI directly into my TV and then the optical cable to my surround sound. I have to turn down the TV volume all the way if I do surround sound, but then I don't have to have my receiver on all the time. If you have an expensive receiver I believe some have passive inputs that will work even if the receiver is in standby to an output HDMI port. I believe they also mute the audio out when the receiver is on to the TV so only the surround speakers are on.