Do I just get on the ts and sit there and listen?

You could, but at most you'd only hear controller coordination and just general banter. (In fact, if the controllers prefer to use other means of voice coordination, such as VRC's built-in intercom system, then you wouldn't even hear that.)

Instead, you'll likely want to download an ATC client (VRC is a popular choice throughout VATUSA), download the sector file(s) from the ARTCC(s) you'd like to observe, and connect to the network as an observer. Within VRC, you can retrieve controller information to determine the voice server and channel a given controller is using and use that to listen in on the frequency.

I think it's more common to address them using the names that matches their VATSIM callsigns (LA Center in your example) and include a brief hint as to which of their many functions is relevant for you.

For example, real world, it might be as succinct as "ground, N123, taxi." But saying "LA Center, N123, taxi" on VATSIM gives no context as to which of the numerous virtual tower cabs the controller should pretend he/she is in. Instead, "LA Center, N123, John Wayne, taxi" is a lot more beneficial.

My $.02.

In that there was no other KSNA ATC position staffed other than Ground, what frequency was I expected to change to and who was I expected to contact?

In the real world, it would be whatever frequency you desire. CTAF, nearby ATIS, GUARD, Fingers, or some random spin-of-the-dial. Essentially, "frequency change approved" means "our conversation has ended (likely since you exited my area of control and there is no handoff to be made); since we no longer have anything to say to each other, feel free to change your radio to whatever frequency you want."

On VATSIM, the CoC (B7) is a bit more restrictive:

Pilots flying through uncontrolled airspace should set their VHF radio frequency to 122.80 or other designated "Unicom" frequency and monitor until they come under air traffic control coverage.

End of conversation on my part, make any other comments as you see fit.  Good night!

Are you taking your ball home with you, too?

I really, really hope that all simulator use magnetic heading.

And I really, really hope they all use true heading, given that true heading is used in all/most written weather observations (e.g. METARs, TAFs, D-ATISes, winds aloft reports, etc.).

This is assuming the tower doesn't have a certified radar display, which in my experience, most Class D towers don't have.

In addition, the cab controllers would have to be likewise certified/trained to use the CTRD for the purposes of providing a radar service (namely radar separation). Not sure if the two are always guaranteed, but I could see how they wouldn't be (and a cursory glance at some admittedly dated StuckMic posts would lead one to believe this as well).

Can you provide references to this information?(AIM, 7110.65)

One reference might be 4-8-1(g) for subsequent approaches. A broader reference would be the separation minima for IFR-IFR in Class D airspace. If the radar controller has to maintain separation, and he can't transfer that responsibility over to tower in the form of radar separation, how can he guarantee the separation without applying one-in-one-out or other nonradar techniques?

ZY: I was half expecting you to suggest everyone brush up on their timed approach knowledge as well.  

I heard three in a very short timespan on KC center freqs. Two were from the same pilot - one on an initial check-in and then the subsequent readback of an instruction.