Jim Dandy: Very good question. Its not very easy to call the difference in those two even if you consider yourself an expert in the area. Sometimes the deciding factor is what the band itself says..

I'd say the biggest difference is in the singing. Death metal uses deeper growls and black metal higher shrieking voices.

Also the lyrical content is different. Black metal lyrics are mostly anti-christian, anti-society or anti-everything. Death metal usually tells about the darker things in life without too much judgement. But if you're not used to listening to the kind of vocals these genres offer it can be quite hard to judge by the lyrics.

Also usually death metal has slower tempos and lower tuned guitars. Death metal bands hardly ever use keyboards in their music and in black metal it is quite usual.

Anyways these genres are like very spicy food. Once you get into them the regular kind seem kind of bland.