I'm attaching a thermostat, and have the correct wires to the correct terminals, but because I'm a bit afraid of electricity, and therefore don't know much, I'm not sure how much of the stripped wire needs to be in contact with the terminal. Also, the wire seems all snug, but the minute I start to tighten the screw, it seems to lose contact!

Is this a low voltage T'stat or baseboard heat type? Baseboard heaters have a 240V t'stat while most others are are low voltage and you won't get electrocuted on these but sure can @240V. The wire around the terminal should go 2/3 around the screw, wrapped the way the screw tightens. If the wire tightens and then loosens, you may have stripped the threads. Sometimes you can get a larger screw with a cutting thread that will re-thread the hole. Otherwise, you may need a new t'stat and they're not too expensive. Some people cheat by putting thin wires in the thread hole and then re screwing it . However, the loose wires can sometimes short the t'stat.

Thanks! It is low voltage, I had the furnace turned off,realized after I wrote question that I was trying to screw the wire opposite the way the screw tightens.\! Once I figured THAT out, I decided most of wire should touch screw and wa-la!

Glad we could help. I find a lot of wires put on backwards, even in DIY magazines! Brian