Protein purification requires separation of one desired protein from all the other proteins translated in a cell. This sounds difficult but is easy when you know the characteristics of the protein. A typical protein purification scheme takes advantage of this unique combination of characteristics to separate the desired protein from all the others. Let's purify an imaginary Protein X that has been expressed in a host cell. Protein X is a large fatty protein with a strong positive charge.
Purification starts with disruption of the host cell to release all the internal proteins.
Next, proteins in solution are pumped past special resin beads in a cylindrical column. Some proteins will stick to the resin and others will pass through the resin bed. Captured proteins can be released from the resin with special elution solutions. The host cells are grown in a large vat like yeast are grown to make wine or beer. The cells were spun out of the fermentation broth using a centrifuge to create a thick cell paste like peanut butter.