This core business is really quite simple. Each core runs one thread of execution at any moment in time. Any program must have at least one thread as their main thread but you may also code up programs to have more than one thread so do tasks alongside the main thread.
So with a dual core and one single threaded program running, it will run at exactly the same speed and the second core will be idle.
With two single threaded programs running you have two threads in total and one will be assigned to each core so each will run at full speed. If you had just one core then it would chop between them constantly and give each program half of its time and so each would run at half speed. Therefore dual core is twice as fast.
You can also have one multi threaded program running and each of the threads would be assigned to a different core so the single program would run twice as fast.
Your PC runs many many background tasks alongside the main applications that you run. With a dual core these applications can run on the extra core so even with one single threaded program it might run just a little faster on a dual core machine.
You cannot simple aggregate the core speeds together. The two combined might be the total capable power but you might not be able to harness all of it with one application if that program was written with one thread.
There is a little more complexity with the hyper threaded processors. These look like dual cores to the software system but they are not actually full cores. You get one full one but bits of it that are not in use by the main thread may optionally and occasionally be used to push more waiting threads forward a bit until it needs the resources of the main core units whereby it stalls again. So you get a little extra oomph but not a lot.
Finally, just for information, ViewingDale is written with multiple threads and the web site has a free graphics test program which will tell you whether it thinks the system is multi core or hyper threaded or not. Its not all that useful unless you want to check your system for compatibility.
http://www.viewing.ltd.uk/cgi-bin/viewingdale.pl?category=test_app