Most processors can be broken down into the two basic groups - Batch Processors or Continuous Flow Processors.

Batch Processors

Batch processing is usually the simplest method of producing biodiesel and it is more affordabe (lower upfront cost) and easier to use. This system is common among smaller start-ups and homebrewers.

A batch system will have a reaction tank or batch reactor that the mixing of your oil/fat, alcohol, and catalyst is performed. There are many variations, styles, systems, and sizes for batch systems. A few types and styles can be found on the following links:

Appleseed style

Commercial Made 

Graham Laming's Eco System 

Various Styles

Most batch systems are sealed for safety, help avoid contaimination, and for energy effeciancy. Alcohol to triglyceride ratios of 4:1 to 20:1 can be found using batch systems although a 6:1 ratio is most common. Reaction temperatures can range from as low of 25ºC to as high of 85ºC with a common temperature of around 65ºC

The common catalyst used is usually sodium hydroxide, but potassium hydroxide is not uncommon. A typical catalyst loading range of 0.3 percent to around 1.5 percent is needed to achieve a good reaction.

Mixing of oil, catalyst, and alcohol in the reactor vessel needs to be thorough in the beginning of the reaction. Toward the end of the reaction, mixing is not necessary to allow for a seperatoin of ester (biodiesel) from glycerol. I have heard of some commercial biodiesel batch producers getting around 85 to 94 percent completions. 

There is also a two-step reaction, with glycerol removal between steps, to increase the final reaction extent to 95+ percent. Higher temperatures and higher alcohol to oil ratios also can enhance the percentage completion. Most batch reaction times range from 20 minutes to just over an hour. If a two-step acid treatment is used for yellow grease and/or animal fats, most batch processors can be slightly modified with the addition of an acid esterification vessel.

In addition to the reaction process most producers will perform a wash on their biodiesel to clean any extra impurities and to also polish their fuel. Water washing of biodiesel in a batch system is usualy the time consuming part of the process. 

Continuous Processors

Most continuous processors are not designed for the common home-brewer due to their upfront cost and high output. Although some batch systems will maintain a continuous system of production with multiple processors. A true continuous processor system performs the reaction rather rapid, compared to a batch system, with a completion of 98 percent not uncommon.

Continuous flow processors usually require being operated on a 24/7 basis, requiring larger capacities to justify larger staffing requirements. In addition, a more uniform and higher quality feedstock is necessary to maintain a consistent uniform product and not to have to adjust a more complex machine.

Most continuous processors provide a level of advantage over smaller producers in that they can pay slightly higher feedstock prices and still be able to turn a profit due to their effeciency. 

Some examples of continuous processors:

Bioking

Biodiesel Technologies

Small Continuous Reactor (may not be a good commercial example)

Methes Energies 

A Continuous Batch Processor (not a continuous processor but continuous batch processor)