A. We use to say how we do something: by post; by phone/ by email; by hand/ pay by cheque; by mistake/ by accident/ by chance etc. (not by the chance/ by a cheque). We use by + noun without the or a.
A1. But we say pay cash or pay in cash (not by cash), do something on purpose (= you mean to do this)
B. use by ~ to say how somebody travels: by car/ by road/ by rail/ by underground. But we say on foot
B1. cannot use by if we say my car/ the train/ a taxi etc. We use by + noun without ‘a/ the/ my’ etc. by car but in my car (not by my car) by train but on the train (not by the train)
B2. use in for cars and taxies. Use on for bicycles and public transport (buses, trains etc.)
C. We say ‘something is done by somebody/ something’ (passive) We say a play by Shakespeare; a painting by Rembrandt; a novel by Tolstoy etc.
C1. Compare by and with: The door must have been opened with a key. (not by a key) (= somebody used a key to open it) vs. The door must have been opened by somebody with a key.
D. By also means beside
D1. Clare’s salary has just gone up from $5,000 a month to $5,500. So it has increased by $500/ by ten percent.