How do you extract oil from a seed or from a plant?

for oil from plants, I'd not reinvent the wheel,you are right nuts are a plentiful source... as in palm, coconut and large exotic nuts of mid-America.

pressing is as it sounds pressing the nuts as in squeeze, another is centrifugal force spinning the nuts under pressure, still another involves heating the nuts... while all of these methods may work however one must factor in the amount of energy used to extract the oil... is it cost effective, in that you might consider using solar, wind, Geo,wave energy to reduce cost.
hope this helped, you may consider contacting BP/Shell company's and talk with them , they give you info and a good direction for your research.

Pressing is literally that.  A hydraulic press expresses the fluid from the solid or you run the meal through two robust touching hard rollers - meal goes through, oil stays behind.

The other route is extraction.  Grind up the source, extract with organic solvent, evaporate the solvent.  Liquid carbon dioxide is also used, and supercritical CO2.

How will you control oxidation of unsaturated oils?  Separate oil from water?  Remove toxic principles (e.g., soybean inosinates).

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From plant matter, one method of oil extraction is by steam distillation.  Check out "steam distillation kit" on ebay for pricing.  Make sure the glassware is made of pyrex.