Commercially, except for the certified "cold pressed extra virgin olive oil", any other oil extraction (including any other olive oil) involves the use of some form of solvent.
The mechanical extraction has a very low efficiency and it's basically done in three steps: grinding the seeds to a pulp, squeeze at high pressure, separate the oil from the water.
I can give you details of the process used for the olive oil since my grandpa used to produce it. Not sure if you can do it at home though...

en.wikipedia.org/wiki/Vegetable_oil

The "modern" way of processing vegetable oil is by chemical extraction, using solvent extracts, which produces higher yields and is quicker and less expensive. The most common solvent is petroleum-derived hexane. This technique is used for most of the "newer" industrial oils such as soybean and corn oils.

Another way is physical extraction, which does not use solvent extracts. It is made the "traditional" way using several different types of mechanical extraction.[11] This method is typically used to produce the more traditional oils (e.g., olive), and it is preferred by most "health-food" customers in the USA and in Europe. Expeller-pressed extraction is one type, and there are two other types that are both oil presses: the screw press and the ram press. Oil seed presses are commonly used in developing countries, among people for whom other extraction methods would be prohibitively expensive. [12] The amount of oil extracted using these methods varies widely, as shown in the following table for extracting mowrah butter in India:[13]

You can get corn oil off the mash that results when you ferment your corn in a sweet mash ferment prior to going to the still. Ya gotta skim the oil off anyway.

You can get olive oil by squeezing the living Jeebus outta your olives.