Friction is your enemy here. There are three places friction will cause these problems: the shifters, cables/housing, and the derailers themselves. If the bike is older, dirty, or just not well cared for, take all the cables off. Clean them and replace as necessary.

Unless the derailers are really dirty or bent/broken, I don't think you'll have too many problems here. Just make sure they're clean. I also don't think it's too likely the shifters are the main issue. But I'd still clean and lube them up as suggested above. Most problems of excessive friction that I've seen are due to dirty or corroded cables.

Shooting WD40 into cables one at a time can tell you which part was causing the problem, as it will usually free everything up nicely. But most people don't recommend WD40 as a solution because it doesn't last long.