The Stage Manager is responsible for co-ordinating scene changes and other technical effects that are controlled from the stage during all performances. On complex shows they may have any number of Assistant Stage Managers and a large team of Stage Crew who will actually execute the scene changes and effects, and the Stage Manager should plan not be doing anything themselves, but just to oversee this team of people, ready to step in should anything go wrong. On smaller shows, it may be appropriate for the Stage Manager to do some or all of this work themselves.
The Stage Crew who work on each performance may not be the same people for every night of a show's run, and it is the Stage Manager's responsibility to ensure any new members of the crew are completely familiar with the jobs expected of them, arranging practice runs of more complex scene changes before the performance starts, if necessary. On complex shows, the Stage Mananger may choose to appoint one or more Assistant Stage Managers, who will be present for every performance, and may look after one area of the stage or one special effect, and train any Stage Crew needed for those particular jobs. It is commonplace in student theatre in Cambridge to call Stage Crew 'Assistant Stage Managers' and to call someone who does all the shows/trains other people on relevant jobs the 'Floor Manager'.
The Stage Manager also forms part of a team with the Deputy Stage Manager, who between them should attend enough rehearsals to familiarise themselves with the show before the technical rehearsal in the theatre. They should try to spot any potential technical problems caused by the blocking or choreography before the show moves into the theatre, and work with the Technical Director to resolve them.
Some shows in Cambridge choose not to have a Technical Director, in which case some of the responsibilities (often the planning of special effects, drawing of set plans, and running the get-in and get-out) can fall to the Stage Manager or Deputy Stage Manager. It is very rare for the set building and painting responsibilities to be taken on by stage management.