If you want to peek at all the details really returned by DiscreteWaveletTransform then do this:

In[1]:= data = RandomReal[{-1, 1}, {8}];
Normal[DiscreteWaveletTransform[data]]

Out[2]= {{0}->{-0.0640216, 0.201553, 0.566641, 0.44696}, {1}->{-0.0263881, -0.110478, -0.650836, -0.449402},
  {0, 0}->{0.0972497, 0.716724}, {0, 1}->{-0.18779, 0.0846273}, {0, 0, 0}->{0.575566}, {0, 0, 1}->{-0.438034}}

Then on the help page for DiscreteWaveletTransform you can click on Details and Options and guess how to interpret this tree information you are given.

This might even help you see how to check to see whether the processing of the results turned out to be correct.