Answer: To be quite honest, tuberoses (Polianthes tuberosa) can be "touchy" to keep over from year to year, and often do not bloom well if at all after the first year, so don't be too disappointed if it doesn't work.
Remove all but about 3 inches of the foliage now, then remove the rest when it is quite dry. Do not remove the offsets until planting time. (They will need a year or two to reach blooming size, so it is up to you whether to keep them or not.)
Some gardeners allow these to dry with a nice lump of soil attached, others prefer to wash them. Washing does provide an opportunity to inspect them for imperfections and any damage which might cause rot during storage. In either case, let them dry thoroughly before storage and keep them dry until they are replanted.
If washed, store them in a cardboard box or paper bag in layers covered with sand or peat moss so that they don't touch. Keep the package in a dark place with good air circulation at about 60 degrees. If they are still encased in dry soil, add enough filler as needed to ensure they don't touch and store a bit cooler.
Good luck with your tuberoses!
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