I'm usually inclined to try and fix things myself. I'll almost always do enough research to at least see what's involved in the task.
I've found that sometimes it's best to let an expert take care of it though. If I'm not familiar with the repair it will take me more time to complete the job vs an expert with experience in the particular task.
I like to try and fix things myself if it is a minor repair, especially if I have an instruction book or can find information on the internet to help me fix it. Now, if it's something that I've paid a lot of money for, or something more complicated to fix, I'd rather pay someone to do it. For example, when I ordered a desk to be delivered, I paid extra for the delivery man to assemble my desk, so that it would be put together correctly (and to save time). It was worth the expense to know that it was done right.
I almost always try to fix it myself. There are two reasons for this, first I always think I can do it, and usually it's not as easy as I think it will be. And second, I'm a real cheapskate and I don't want to pay someone to fix it.
I pay somebody else to fix them. I used to be a real do-it-yourselfer, but these days my time is too valuable to me to be messing with something that's broken. I'll either just replace it or support the local economy and call the local "fix it" guy for whatever is broken.
It depends on what it is really. I've fixed my dryer twice. Once I replaced the heating element, and the second time I replaced the drum belt. I've also fixed my car on occasion, but they were easy fixes like adding oil, or changing spark plugs. If I can research it, and find out how to do it, and it's cheaper to fix it myself, then I refuse to pay someone to do it. lol