A typical dialysis procedure for protein samples is as follows: 
# Prepare the membrane according to instructions
# Load the sample into dialysis tubing, cassette or device
# Place sample into an external chamber of dialysis buffer (with gentle stirring of the buffer)
# Dialyze for 2 hours (at room temperature or 4 °C)
# Change the dialysis buffer and dialyze for another 2 hours
# Change the dialysis buffer and dialyze for 2 hours or overnight
The total volume of sample and dialysate determine the final equilibrium concentration of the small molecules on both sides of the membrane. By using the appropriate volume of dialysate and multiple exchanges of the buffer, the concentration of small contaminants within the sample can be decreased to acceptable or negligible levels. 
For example, when dialyzing 1mL of sample against 200mL of dialysate, the concentration of unwanted dialyzable substances will be decreased 200-fold when equilibrium is attained. Following two additional buffer changes of 200mL each, the contaminant level in the sample will be reduced by a factor of 8 x 10 (200 x 200 x 200).