A previous poster said to use methylated spirits and toilet paper. The first part is correct, the second part is somewhat risky.
Methylated spirits are also known as "Mineral Spirits" or by the brand name "Varsol".
Mineral spirits will easily remove fingerprints from most non-porous surfaces. They do this by dissolving the residual oils left from your fingers. You should wear latex gloves while doing the work, as the solvent will defat your skin, and can damage it. Be cautious with plastics - some plastics are dissolved by mineral spirits. Test first.
The optimum material to use to rub the fingerprints off the block is an old piece of T-shirt - MUST be 100 % dotton - that has been washed and dried several times. This material will not scratch the base of your heat sink, and won't leave any lint behind. The old T-shirt trick is something that is widely used to clean photographic lenses in a pinch, as it won't scratch the glass or leave residue behind. HS blocks are most effective when smooth and polished - scratching with toilet paper or paper towels is a good possibility.
Mineral spirits are quite volatile (evaporate quickly) and flammable. Use in a well ventilated area and no smoking while using them.
Hope this helps