How do I search my calendar for a specific appointment? For instance, if I want to recall a date when I had an appoinment with the Apex Company, how do I find it? Also, if I'm sitting in a meeting that I currently have on my calendar and they schedule the next meeting, how do I go to that date to schedule it without re-typing everything?

There is a program called search. This allows you to do so. It is standard on all OS

If you don't mind losing the calendar appointment of the current meeting, you can go to the current meeting and simply change the date of it, to the newly scheduled meeting.

Or, to save the history of the current meeting, go to the current appointment, select and copy the text you need, close that appointment and open a new one, paste, schedule the new one, etc.