This can be accomplished either by hand or with a stand mixer using a paddle attachment. For small quantities of forcemeat, I've found that hand mixing does a better job than machine mixing with less clean-up required. For the home cook, a food processor must substitute for the horizontal or vertical chopper used by the professionals. Additionally, the bowl and blade of the food processor should be chilled in a refrigerator before using. Some mechanical stuffer is required.
Some grinders have sausage stuffing attachments that can be used for occasional projects.
Small commercial stuffers are available from restaurant supply stores at a reasonable price. No matter what type of stuffer is used, it is important to be sure to pack the meat mixture into the stuffer without creating air pockets. Air pockets result in air bubbles in the finished sausage. Use the largest stuffing tube that works with the casing being used so that the meat mixture is not heated by forcing it through too small of a tube. Sufficient casing is slipped onto the stuffing tube and a knot tied in the end before the stuffing starts.