Quick search provides us with three most common methods.
I would think that the people on this site could come up with a backyard way to produce fuel for our trucks.
Method one seems the easiest.
Expeller/Press
Expression/Expeller press-When algae is dried it retains its oil content, which then can be "pressed" out with an oil press. Many commercial manufacturers of vegetable oil use a combination of mechanical pressing and chemical solvents in extracting oil.
While more efficient processes are emerging, a simple process is to use a press to extract a large percentage (70-75%) of the oils out of algae.
Hexane Solvent Method
Algal oil can be extracted using chemicals. Benzene and ether have been used, but a popular chemical for solvent extraction is hexane, which is relatively inexpensive. The downside to using solvents for oil extraction are the inherent dangers involved in working with the chemicals. Benzene is classified as a carcinogen. Chemical solvents also present the problem of being an explosion hazard.
Hexane solvent extraction can be used in isolation or it can be used along with the oil press/expeller method. After the oil has been extracted using an expeller, the remaining pulp can be mixed with cyclo-hexane to extract the remaining oil content. The oil dissolves in the cyclohexane, and the pulp is filtered out from the solution. The oil and cyclohexane are separated by means of distillation. These two stages (cold press & hexane solvent) together will be able to derived more than 95% of the total oil present in the algae.
Supercritical Fluid Extraction
This can extract almost 100% of the oils all by itself. This method however needs special equipment for containment and pressure
In the supercritical fluid/CO2 extraction, CO2 is liquefied under pressure and heated to the point that it has the properties of both a liquid and gas. This liquefied fluid then acts as the solvent in extracting the oil.