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There is now a separate page devoted to repotting and for an illustrated step-by-step description of the process, you should see the Repotting page.  A brief outline is presented here.  There are a couple of rules about repotting. The first rule is to repot when your plant doesn't look good.  Don't worry about throwing off the spike cycle or anything like that.  If your plant looks like it has a problem, take it out of the pot and carefully check it out.  Usually you will find root problems this way.  You can then remove the dead and/ or decaying material,  treat it with a dilute fungicide, and pot it up. I usually hit the problem area with a very hard spray of water using maximum hose pressure through a 4 gal/minute Fogg-It nozzle. This won't hurt any good healthy material but washes away some of the decaying material.  You have to support the plant a bit though when you do this or it will take the roots right off.  I use a piece of plastic fly screen or window screen in a frame that exactly fits the sink.
The second rule is to repot at least once a year.  The optimal time is after blooming but before the middle of Winter.  I used to let this go longer but there is a good reason for separating the new plant from it's old decaying parent.  The longer the plant sits and soaks up sunlight in the winter, the better the tuber and the stronger the flower spike the following year.  In the northern hemisphere, you should be finished repotting by Christmas.  You don't necessarily want to do it the minute that the bloom is finished but there should definitely be new growth starting.  If I can't see next year's growth, I put the plant to the side and leave it for the last batch to be repotted.  Usually by then something will happen.  If it still doesn't have any new growth, you can take it out and look at the roots, but you probably have lost the plant.  This kind of goes back to rule one.  If you have a blooming plant with no new growth that isn't just a second year plant that has never made a tuber, you might want to tip the plant out of the pot and see why no new growth is being formed.