There are different methods available for isolation and purification of enzymes from a given source like salt precipitation, different types of chromatographies notably ion-exchange,affinity, GFC or HIC etc. The choice of method is decided by the physico-chemical properties of the protein under question e.g., Mol wt, isoelectric point, presence of affinity tag or hydrophobicity. Isolating a protein generally requires a combination of two or more steps which have to be determined and optimized experimentally.
Now coming to your question, protease isolation from fruit juice has been achieved by ammonium sulphate precipitation followed by ion exchange chromatography (do not forget to dialyse away the salt after dialysis, otherwise the protein will not bind to the exchanger).
[ for reference : International Journal of Pharmacology and Toxicology, 1 (2) (2013) 82-90]
Different properties of proteins are exploited for protein purification.Enzymes being protein can be purified by exploiting the properties of protein like solubility , molecular weight, charge on protein etc.