To carry out a compression test first you need a compression tester. Buy, rent, or borrow one. Remove the spark plugs of the engine you are testing, insert the tester into a plug thread (it should be obvious how it's done, or you will have an instruction booklet), and spin the engine over. make a note of the reading and which cylinder you measured, then repeat on all the other cylinders.
Then repeat the process after squirting a little engine oil into the plug holes (about an eggcupfull).
you should be looking for differences between individual cylinders, typically you should have reading between 120-160 psi. The readings should noticeably increase with the wet test (oil in the cylinders) as the oil will have the effect of helping the piston rings seal, if not then you may have valve seat issues or possibly a leaking cylinder head gasket. if it makes a big difference you could hang ring or bore wear issues.
An engines compression ratio is the difference in combustion chamber volume with the piston at tdc and bdc. To alter an engines compression ratio you will have to dismantle at least some of the engine, piston design, cylinder head shape, connecting rod length and head gasket thickness all are factors in determining what a compression ratio will be.
Roger.