It depends on what kind of fridge you have, and therefore what style of icemaker how easy the home repair could be. I have a side-by-side fridge, and have had my ice maker quit a few times with varying solutions (it's from 2001, and still in great shape, so definitely worth fixing)... (these are all for side-by-side fridges and may not apply to stacked)...
1) A chunk of ice is jamming the mechanism. It takes a surprisingly small piece of ice to do this... if mine stops, this is the first thing I check - stick my hand right in the grates that make the cubes and fish around - this is the problem most of the time
2) The line froze-up somewhere... this is a bigger pain. Root around and find the line leading to the mechanism.... if there is any bit of frost on it, that could be the issue... the solution is start with a hot wet washcloth to the line, if that doesn't work then defrost your fridge (old skool, I know)
3) A part actually failed... Ice makers aren't complex creatures, and many of the pieces are little plastic bits, or little switches that maintain the temperature. If you are handy, you can probably research online and figure out the part. I consider myself to be darn handy, but I've called out this repair. For me, the temp sensor failed - $150 ish (the guy was there literally 7 minutes. GAH)
4) It's something bigger and more insidious. I *just* had this happen right after New Year's. My ice maker stopped working... I was super busy and #1 wasn't the issue... I hadn't had the time or desire to do #2 yet, and when I came home one day, about a week later, the whole fridge was kaput. Fortunately for me, I have a fridge in the basement (oh, the luxury!) AND a home warranty... so I called the warranty people, and a Sear's guy came out and fixed it (again, some small part, but without the warranty it would have been $225).
It's usually something quite simple - and if you have the right book/manual/online site, you can probably figure out the repair yourself. In my experience, it's $100 just to get a guy to your house, plus labor and parts, so probably a minimum of $150 for any professional repair.
If you have Angie's List, you can check there - I've found some great folks thru them...
GOOD LUCK!!!