I dealt with Clearance Delivery the other day at Salt Lake for the first time. I was heading from inside Salt Lake Class B to Provo Municipal, a Class D. It pretty much went like this:
Started up. Grabbed the ATIS. Called Delivery.
"Salt Lake Clearance Delivery, Skyhawk 12814, VFR to Provo with Oscar."
They called back, and gave me a clearance, route, altitude, frequency and transponder code. (C-R-A-F-T)
"Skyhawk 12814, cleared through Bravo airspace via the I-15 southbound transition. Maintain 5,500 while in Bravo. Departure on 120.9, squawk 0326."
"Cleared through Bravo via the I-15 southbound transition. Maintain 5,500 while in Bravo, departure on 120.9, squawk 0326."
After I was told 'readback correct', I taxied out to a part on the ramp just before the ramp / taxiway boundary.
Called up Ground with who I was, where I was and what my intentions were. I don't know if it's standard at other airports, but at KSLC there are blue squares with white numbers on them for location identification. You call up ground and tell them what spot you're at.
"Salt Lake Ground, Skyhawk 12814, spot 26 with Oscar. Request taxi, VFR southbound."
They gave me taxi clearance, and then it was just normal departure from there.
Hope that helps a bit.