I have 10 years experience working as a conceptual designer for the Financial Mail and some of their supplements.
First step would be to read a detailed brief, then discuss with client to get clarity in general, timelines for the project and generally what’s expect from you. Gathering the correct specs include print (size and other requirements)/digital (size and other requirements), colour schemes, colour settings if any, material (graphics, copy, pictures, etc.) would come next. Roughs with pen and paper follow to bash out ideas/layout. Once I’ve distilled some designs I would get two-three of these digitized. Once in digital form I would play around some more keeping the mind to not to lose the message I’m attempting to communicate and judging the aesthetics as I go along. Depending on client’s willingness I like to get them involved in the process of design elimination, corrections and tightening up the design. After corrections and design tightening up process client has to review (again) and give feedback then once happy proceed to the final stage of handover.