How to use reed switch to change operating modes?
A reed switch and magnet is the same electrically as a pushbutton switch. The rest is simple interfacing and programming a micro (or designing a logic circuit with debouncing and some flip-flops or whatever to retain the states, but a micro would be, by far, the most appropriate solution in the real world). 

Speaking of the latter, if this is a homework problem, please show the actual question and your attempts to solve it.