Its long way to go I'm afraid, start with ion exchange followed by gel filtration, another ion exchange step maybe required at the end. these are the common protein purification steps that I personally prefer to use for enzyme purification, others such as ammonium sulphate precipitation is used as first step. I assumed that you are using non cloned protein, you need desalting steps several times especially after the last step before assay, you also need to monitor purification progress on SDS PAGE so keep (save) a small volume after each purification step.
The general approach goes like this: Begin by cloning the enzyme, or having the gene synthesized, and overexpressing it. The construct should have an affinity tag, such as a His-tag, as an aid to purification. If it is a soluble enzyme, then make every effort to overexpress it in a soluble form. Then break open the cells by one of several methods in the presence of protease inhibitor cocktail. Then the purification can begin. This will involve one to three chromatography steps. If overexpression is high, it is usually possible to follow the protein through the purification by running fractions on SDS-PAGE.
If the gene for the protein is not known, then you will start at the point of breaking open the cells. Since the protein will not be a major band on SDS-PAGE at the beginning, you will follow it through the purification by measuring its enzymatic activity in each fraction.
There is plenty of reference material available to introduce the basics of the methodologies. Here is one site to look at, for example:
I assume the enzyme you want to purify is not characterized to allow it to be cloned yet. However the type of enzyme should be known. Then you can find possible substrates in the enzyme database
http://www.brenda-enzymes.org/index.php
The link given by Adam could help but the help provided has to be purchased.
I would suggest to consult a recent textbook on enzyme production and purification. In our book "Biocatalysts and enzyme technology" from 2012 we have a chapter on this and many references to recent literature. The flowchart to be followed is given as an attached file. More information on the the problems tat has to be solved to achieve enzyme purification you will find in the chapter that I can send you privately if you give me your e-mail. For ion exchange or mixed-mode (hydrophobic adsorption and electrostatic desorption) chromatography (cheaper and easier to use than affinity required for his-tagged proteins) you need to know the isoelectric point of your enzyme that you can determine with isoelectric focussing. Before chromatography you should concentrate the clarified homogenate by ultrafiltration. Salt precipitation should be avoided as the salt has to be removed before ion exchange or mixed-mode chromatography.
I second Adam's answer with a major modification. Rather than following your enzyme by SDS-PAGE, I would monitor column purification fractions either by western blot (if you have a mAb specific for your target protein) or use an enzyme assay specific for your protein. Either of these approaches is far more powerful than SDS-PAGE especially during the early stages of purification when you may have several contaminating proteins migrating at the same apparent Mw as your target protein (which could be different from the real Mw, the reason why Mw should never be determined by SDS-PAGE. But this is a different story...).