Once you arrive at the terminal a porter will check your baggage tags and take charge of your checked baggage. You will not see these until delivered to the hallway adjacent to your cabin (generally they usually arrive at from late afternoon to early evening).
Upon entering the terminal you will be directed toward a single (integrated) TSA security screening queue. This is very similar to the airport, and all passengers, VIP included, need to pass through the carry-on bag screening and the body magnetic scanner. You will have to show your Fun Pass and ID to go through security.
Once through the security screening you can proceed to the VIP Lounge or Designated VIP check-in line(s) amidst the regular check-in lines. VIP Lounge availability and location varies from terminal to terminal. For instance, in Miami the VIP lounge is to the left of the main check-in and waiting area; the door is small and not particularly well marked. When you enter a roving receptionist (with an official clipboard) you approach you and ask for your name and Fun Pass. You will then be listed on the clipboard in order of arrival and invited to take a seat in the lounge and help yourself to light refreshments while waiting to be called up to the check-in desk.
When called, you present your Fun Pass, CC, passports/IDs and will then be issued your S&S Cards and a cutaway deck plan/map of the ship. You then leave the lounge and proceed to the ship boarding area where you re-queue with the other passengers to pass through the boarding photo zone (optional), and then queue up for entry into the lobby/atrium area where your photo for the S&S Card will be taken (this is mandatory).
As you can see, VIP processing only skips one part of the total check-in/boarding process. I have done Carnival VIP twice and regular once. They all took about the same amount of time; in my experience the differences from port-to-port (some are just slower than others) is much greater than the VIP/NON-VIP differences.