Set Design, Construction, dressing and demolition tends to be the realm of the stage manager though techies and actors are often persuaded to weld a power tool or paint anything that doesn't move fast enough.
This is where you speak to your director and find out what it is they want. then you hit them about the head a few times and inform them that floating carpets and a revolve and a 2m fireball are not going to be possible on a £15 budget.
Speak to the set manager and other stage managers especially if you are on at the same time as another show to find out early if there are going to be any major conflicts.
a useful tool is Google Sketchup, a 3D modelling program that lets you quickly move blocks and pieces of set about and see what it will look like without getting tired.
Bribe as many other techies and stage managers to come in and build your monstrosity. usually taking all night and ending with lots of tired folk and a metric tone of sawdust.
At a bear minimum all wood must be painted (for fire protection reasons) and all fabric flam checked. Though you probably want to do a bit more than that. This is the point where you let your artistic ability's go wild and make your set look really pretty. Or you are to tired to do any more work and you the words 'meah' and 'it'll do' get uttered. Actors are good at painting stuff and most techies (especially tech-managers) shouldn't be allowed near gloss paint.
Undo everything you have spent the last week or 2 creating in one evening and leave the theatre nice and tidy.