Carving tools--non-powered, anyway--are simple. Most consist of a handle of wood or plastic, and a very, very, very sharp steel blade in one of many shapes. The tang is a smaller portion of the steel that is fixed inside the handle. Some pull apart easily, others don't. For the most part, plastic handled carving tools have more readily removable blades, and often come in kits that allow the carver to use one handle with many tool shapes, thus saving money.
The tool handle sometimes has a metal ferrule at the tang end. For heavier duty use--sculpting style carving--a heavier, ferrule is sometimes fitted to the top end of the handle to limit damage to the handle when it is struck with a mallet. Between the blade proper and the tang may be a shaped section: this shoulder is known as a bolster. The extra metal here prevents the tang from being jammed into the wooden handle.
Carving tool blades come in two primary configurations: flat chisel types, or curved in cross-section for use as gouges. A flat chisel for carving has two bevels and each side looks the same. A gouge has a concave surface and a convex one. The concave side is known as the inside or channel of the gouge. The convex surface is the outside or back.
Going towards the tip, past the bolster, is the shank which precedes the various shapes of blades.
At the working end of the tool, a bevel brings steel thickness down to a cutting edge. In some tools, there may be an inner bevel and an outer bevel. The spot where the bevel meets the full thickness of the blade is known as the heel.
Not all these parts need equal care, but all good tools, including carving tools, deserve reasonable care.
You may wish to store your carving tools in a box, including the one they came in, or you may find that using a tool roll is your best bet. A good tool roll is a big help to keeping carving tools in shape, at hand, and easy to use. Tool rolls are available for micro-carving and regular carving tools. Tool rolls serve to protect your fingers, by placing the shank where it can be properly gripped, and the tool's edges, by encasing the sharp bits in canvas. You may also build an eye-level shelf, or a rack designed to hold your tools, with spaces for any extras you may gather in the future.
Last month's emphasis was on sharpening, so you're on your way there. Get the tools sharp and keep them that way with maintenance strokes during and after a carving session.
If a handle or blade problem unrelated to sharpening occurs during a session, deal with it then, rather than letting a lot of small concerns build up. You want to get your tools feeling so comfortable and working so well that you don't really think about them when they're in use. Start by putting a really great edge on all tools when you first get them.
Put your carving tools away in the state in which you want to use them next. Pulling out a tool that needs sharpening is frustrating and finding a cracked handle, or a slipping tang, is even more irksome. Keep the tool sharp during your session, and give it a stroke or two, or three, as you put it away. If you make that a habit, or a rule if habits aren't easy for you to form, you'll save energy and be in a better mood.
Return tools to the box or roll as soon as you finish using that particular tool, not when the session is ended. That saves some time, and keeps the carving bench clear of sharp edges. Don't forget to stroke that edge and give the tool a wipe with an oil rag, or a shot of Top Cote or Boeshield (which I prefer to using oil where it might contact wood). If you use the oily rag, use a clean cotton cloth to wipe the tool off before its next use.
Protection is to prevent mechanical damage, especially to the cutting edges, and the effects of dampness. Carving tools that are used nearly daily will not normally rust. The longer your tools are unused, the more protection they need from dampness. This matters most to carvers working outside their homes, but a quick touch up with Top Cote or Boeshield T-9 for storage in damp spots helps prevent rust. Whenever possible, keep the tools in the house environment.
Working as above will help you keep your carving tools in shape and ready to go at a moment's notice, while also making your work area safer and more pleasurable.