Does Clearance Delivery operate in the same way for airports in Bravo, Charlie and Delta airspace?
All will be pretty similar.  In Bravo, and Charlie and Delta if they are close to the Bravo, you will typically contact Clearance for your departure directions (heading to fly, altitude to climb to or hold at after takeoff (or cleared to climb to 1, and expect clearance to higher after so many minutes, or when reaching some intersection), and Approach frequency to expect) before Ground gives you clearance to taxi from parking towards the active runway and for your runup.  If you filed a Flight Plan, expect to have the clearance (perhaps modified) read to you, which you must read back. 
After switching to Gnd for Taxi directions, be ready to read those back as well. Have the Airport Diagram out, and don't be afraid to ask for Progressive Directins.  Things can be busy at a Bravo. When your runup is done, you switch to Tower if Gnd hadn't handed you over already, let them know where you are and that you're ready for takeoff.

If the Charlie and Delta are not near the Bravo, things may be a little more relaxed. You may get your Clearance from the Tower, or Gnd, and Gnd/Tower may be the same guy on the same frequency, or he may be on 2 or more frequencies, switching between Gnd and 1 or more Tower frequencies for different air sectors.  You may stay on the Tower frequency longer before being switched to Approach, or for Delta you may just be asked to advise when you are clear of the Delta airspace.

Don't fly to any Bravos until you are comfortable on the radio.  Limit flights to Delta and Charlie to start until you can follow the lingo.