First off: Even Andrew Kramer, king of After Effects, simply goes through all blending modes to find an appealing effect. So playing with them is a really good option.
There are common uses for some blending modes, though:

Screen and Add both make dark parts of the image transparent. (That is, the color from the layers below will show through dark parts.)
This is often used for explosions on a dark background, since you only want the bright parts of the explosion to show.
The difference between those two is that Add really adds brightness. If the bottom layers have a fairly bright spot and the layer on top (with the Add blending mode) is fairly bright in the same place, the result will get even brighter and might clip. With screen, you will simply see the brightest one - either the top layer or those below.

Multiply is the complement to Screen. Bright parts will become transparent. You can often use Multiply on a vignette layer (although I encourage you to experiment!). Substract is not used nearly as often as Add, but should have the opposite effect.

Overlay acts similiar to Screen and Multiply but makes grey (50% brightness) transparent. Images of cracks for compositing purposes often come on a grey background, since you need the highlights and shadows simultaneously for a convincing effect. Apparently, Hard and Soft Light also eliminate grey, but have a stronger/weaker effect - just try them!

I also use the Difference mode to align layers. If, for example, I have two images that were shot on a tripod but do not align perfectly, I put the top one into Difference and nudge them around until I get an image that is as dark as possible.

Those are the blending modes you will use most commonly. But, as mentioned above, it is a good habit to play around by simply scrolling through them. Most of them are pretty specific and I do not really understand them, but sometimes Vivid Light just simply works best, or I choose Hard light rather than Overlay for a more 'dramatic' effect.