I'm having problems with my new Mac (OS X 10.5.2). Its only about 2 months old, I am just getting my head around it as I was a PC user and now with just about every application when I try to open it, I get a window telling me that the 'application quite unexpectedly'.

I have no idea where to start trying to sort this out - can anyone help?

It can be of many causes, check the -/Library/Logs and look for the CrashReporter sub-directory. Inside one of these folders will be the crash.log for what keeps quitting. Read it and it should tell you why.