Create a drawn layout of the set that locates all of the set pieces from either a top-down view or, even better, a three-quarters view from above. Draw a different version for each scene and indicate exactly where each set piece should be. This is particularly important for productions that have lots of set changes.
Create a written inventory of all of the set pieces used throughout the production and exactly where they should be on stage. Use stage directions to indicate these positions. "Upstage" refers to the back of the stage while "downstage" is the area closest to the audience. Stage left and stage right are directions dependent upon the actors' view of the audience while standing on stage ("stage right" would therefore be on the audience's left).
Go through each scene with the set on the stage and lay down two or three pieces of spike tape at the corners of each set piece. Move on to the next scene and then do the same thing. Use a different color for any set changes that occur. For example, all of the set pieces for act one might be marked with green tape, while the set for the next scene may be spiked with blue tape.
Mark each set piece with a small piece of tape that indicates which acts or scenes the set piece is in. A table that shows up in two different scenes with a set change between them should have two different colored pieces of tape on it. Mark them in a discrete location out of the audience's line of sight, but make sure that the running crew is aware of where to find these marks.
Run through the performance only running set changes (cutting out any dialogue or acting) so that the running crew is familiar with which scene the colors denote and where each set piece is moved to. Run through the play this way at least two or three times and then try a full rehearsal with full scene changes as if there were an audience. This will let you pick out any trouble spots and set props that may need to be re-spiked in a new location.