How long do you wait before taking corrective action if your fermentation doesn't start? Are there any other good ways to tell if it's just taking a while to get going?
I generally wait a few days before worrying at all. I have had slow fermentations, where I didn't see any activity in the airlock, but when I took a hydrometer reading after about 10 days, fermentation was complete, so definitely don't assume you have problems simply because you don't see any airlock activity.
Most importantly, make sure your wort is in the appropriate temperature range for your yeast. If you don't have a stick-on thermometer on your fermenter, you should probably get one, they are very inexpensive.
As with all things in this hobby, relax, don't worry, have a homebrew! Remember that people have been brewing beer for centuries without worrying about all of the technical details we get to fiddle with today!
I'd say if it doesn't start in 3 days, then bring it up to the higher end of what the yeast likes, then wait another day or two.
If you still don't see any activity, take a gravity reading, if you're still at your OG then you're stuck.
There are some yeasts out there, Wyeast's saison yeast comes to mind, that ferments incredibly slow at room temperature, which is why you should take that gravity reading before repitching.
Just to add to the other great answers here, I don't think there's much risk in just waiting a few days. I once waited a week (I was out of town) before discovering that I had used some dead yeast. I re-pitched, and when the batch was finished I couldn't tell any difference from previous batches. As long as you keep things sterile it can sit for quite a while with no issues.
First thing I always do is stick it somewhere warm or wrap my fermenting vessel in a blanket for a day. The two times I've had a stuck ferment, that's restarted it.
I'd also be taking hydrometer readings carefully at this point, to see if it really is stuck, or just slow!
Depending on what I'm brewing I expect to see bubbelage within a few days or even less. Sometimes its hard to tell if its stuck or slow. For mead my normal technique is to use a heating pad to warm it up to 70 degrees for so if it doesn't get going within a couple of days.