How to use the phrase "尝一尝"?
尝 basically means to taste something.


尝一尝 = to have a taste of something


Usually it is used quite literally, i.e.: to do with flavors and tastes of edibles.

Here is an example sentence from New Century E-C:


  很多人出于习惯往食物里加盐, 都不先尝一尝。
  Many people add salt to their food out of habit, without even tasting it first.


You can find a bunch of examples from TV show subtitles here:


  Yeah? Take a taste.
  尝一尝





  you can taste it
  你可以尝一尝


etc.



试 on the other hand means try.


试一试 = to have a try at something


Here is an example sentence from New Century E-C:


  这有点儿不靠谱, 但我想我会试一试。
  It's a bit far-fetched but I thought I would give it a shot.