I am looking to freeze the mushrooms that I picked this morning. One website tells me to fry them in table fat. What is table fat?
It looks like Table fat" refers to any kind of solid fat, such as schmaltz, butter, margarine, etc.that you might use at the table, as opposed to cooking fats like oils or lard. One 1917 cookbook notes that "rendered beef fat" is rarely used as a table fat in the US,but is often spread on bread like butter in parts of Europe. (The cookbook goes on to note that more peopleshould use beef fat inpkace of butter to save money--butter now costs almonst 50 cents a pound,but beef fat can be bought for 15 cents or less.) It also does seem to be an older UK term for fat rendered at home or for lard. More modern recipes seem to use it instead of saying "butter or margarine".
To freeze mushrooms
Select medium and small mushrooms with white, tight caps; prepare and freeze the same day as picked or purchased. Handle carefully to prevent bruising; wash well in cold water and drain thoroughly. Do not soak. Cut off the base of the stems and sort for size. Leave whole, slice or quarter. Mushrooms should be blanched or steamed before freezing. An alternate method is to sauté mushrooms in butter or margarine before freezing.
To blanch
Blanch whole mushrooms 5 minutes, buttons or quarters for 312 minutes and slices for 3 minutes. Add 1 teaspoon of lemon juice or 112 teaspoons citric acid to each pint of blanching water. Cool promptly, drain, pack into containers, seal and freeze.
To steam
Mushrooms to be steamed have better color if given an anti-darkening treatment first. Dip for 5 minutes in a solution containing 1 teaspoon lemon juice or 112 teaspoons citric acid to a pint of water. Then steam whole mushrooms for 5 minutes, buttons or quarters for 312 minutes, and slices for 3 minutes. Cool promptly, drain, pack into containers, seal and freeze.
To sauté
Heat small quantities of mushrooms in butter or margarine in an open fry pan until almost done. Set pan of mushrooms in cold water to cool promptly. Pack into containers, seal and freeze.

Not everyone will know what nutrax means by schmaltz. It's rendered chicken fat. There were Jewish meat restaurants in New York that used to keep jars of it on the table in place of butter (which can't be eaten along with meat under the rules of kashrut). Sammy's Romanian is the only place I know that still does that (assuming they still do).