The above was solid advice, however if you're looking for an easier approach then read on:

Right, to start off with use the program for that limit, so if it has 15 uses, open and close the program 15 times, then open it for the 16th time, and note down what message box (if any) error you get. If it says something like "Your trial has expired" then you should use your debugger (I use Ollydbg) or dissasmbler, and set a breakpoint (if you're using a debugger) on that string reference, then when you land there, look above the 'bad-boy' string ("Your trial has expired" for example), and look for any conditional jumps and go from there (hopefully there will be a conditional jump very close by, that will jump away from the bad boy code if you turn it into a straight jump (EB)).
I'll write a more in-depth tutorial with an example program for you when I get chance.
Hope this helps.

P.S. - The website mentioned by least can be found below:
hxxp://krobars.reverse-engineering.info/