I rendered a bunch of fat down to make soap. Here's a tip, it renders faster if you cut the fat up into small pieces.

I had lots of steam coming off my fat when I started, but no smoke. Later, the grease was boiling hot, and the cracklin' pieces were frying, and I still didn't have any smoke. If you are worried, try putting a thermometer in it so you know its below smoke point.

I rendered mine on medium heat on my electric stove. I even added some water at the beginning to get it started. It took about 4 hours (it was a REALLY big pot of fat bits). I fished the cracklins out with a sieve, strained it through a coffee filter to remove any stray particles. I ended up with about a gallon of rendered lard/tallow. It made lovely soap.

I have heard the microwave is good for rendering fat, too. But I haven't tried that.