Phenetics attempts to classify organisms based on overal similarity, typically in morphology, without regard for their evolutionary relationships. Basically, it's classification based on how similar to the organisms look. A single catagory in a phenetic classification system may contain organisms that have different evolutionary histories but have developed similar morphological features through converent evolution.
Cladistics attempts to classify organisms based on their evolutionary lineage. In a cladistic classification system, a single catagory, known as a clade, contains the most recent common ancestor of all organisms in the clade as well as all organisms decended from that ancestor. The organisms in a single clade may be morphological different, but they share an evolutionary relationship. Organsims that have developed similar morphological characteristics through converent evolution will generally be in different clades.
So in summary, the basic different between phenetics and cladistics is that cladistics is based on evolutionary relationships whereas phenetics is based on morphology.