Depending on the type of matrix, soaking in water may loosen up the fossil.
Fossils can sometimes be removed from their matrix by using full strength
vinegar.  Soak the specimen for a long time.  Brushing with a toothbrush
helps loosen material.
 
Usually, it's a matter of patience using fine chisels and picks.  A Dremel
power tool is great.
 
Don't feel you have to necessarily remove all of the matrix however.  Many
of my fossils are still in the original matrix.
 
John L. Jacobs
Seffner, FL
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