Protein purification is assess using various cinematography techniques and spectroscopic methods. It depends on the protein, and accordingly the methods were employed.
Could you please explain what you exactly mean by "protein purification"? You may mean the (im)purity of your extracted enzyme-protein, or the total levels of purified enzyme-protein complex?
You have to be able to determine level of your protein (e.g. measurement of activity, Western blot) and amount of total proteins (pretty easy with plenty of methods). From this you calculate specific activity (or some equivalent for blotting) and this should increase with purification.
I want to let you know that I mean to remove out the junk proteins sequentially and concentrate the enzyme protein of interest. Here I am not talking about whether it is unit enzyme or enzyme-protein complex. as far as enzyme-protein complex is concerned, the bound enzyme can be purified through affinity chromatography.
Dear Dr. Sanjay Mishra the best way to assess protein purification is by doing sdspage after each purification step so you can follow the purification of your protein and check the presence of contaminant. You way need to know some molecular features ex. molecular mass, pI etc. If you are also interested to check if the activity of your enzyme is preserved you may also need to test the activity of your enzyme to make sure that your protein is not denatured through the purification process.
I agree with Mr. Malih... The best way will be to do a SDS-PAGE (Tris-Glycine or Tricine, depending on your resolution requirement) and stain it with Silver staining method. Since silver staining is sensitive than the coomassie staining, you will get to know even the minor contaminants. I hope this will help you.
The same samples you use for silverstain can also be analyzed using SDS-PAGE + western blot. It is best to use another antibody against your antigen of interest, to confirm that the bands you see on your silver stain are your antigen of interest. Additionally you could use your antibody used in affinity-chromatography as your primary antibody on western blot as well, to see if the antibody itself has some cross-reactivity, and is causing the contamination in your 'purified sample'. If you see some inexplainable bands on silverstain that are not recognized by the antibody you used in your affinity-step, I recommend additional washing steps (Triton) before you elute the enzyme from your column.
To calculate -fold purification at every step of a purification procedure, you would determine the specific activity at every step. Specific activity = activity per mg protein. Then at each step, divide the specific activity by the specific activity of the beginning material.