I clean my tubing right after I use it. For example, lets say its bottling day. I use an autosiphon and tube to rack to the bottling bucket, and the same tube and bottling wand.
After racking, I immediately rinse out the carboy and after getting the easy gunk out, fill it full of water and oxiclean and let it soak.
After everything else is done, I rinse out the bottling bucket and then fill it full of water and oxiclean. I submerge the tubing in it and anything else that needs to be cleaned (stoppers, hydrometer). Then i hook the tubing up to the autosiphon and run the oxiclean water through it, for quite a while. Then empty the bucket and rinse it out thoroughly. Fill it full of clean water and run the clean water through the autosiphon and tubing to rinse it thoroughly. When its done, disconnect the tubing and hang it from a rack i have in the ceiling, so it dries.