I did a bit of carving years ago, no great expertise, but do turn wood and occasionally add carved decoration. I suspect most woodturners who sell (hence time=money) avoid carving because it slows the process down. The book referred to above is good - I stumbled on a copy in a charity shop and it was 30p well spent.
Carving and colouring complement each other. I think colouring is often over-used, "let the wood be wood," but sometimes it's the right thing to do especially if the wood is bland. 2 starting points for early attempts. Make a wide rimmed bowl or platter, face it off but don't hollow out the centre yet. One way is to spray the rim with ebonising lacquer and carve through it, you get great contrast. The other way is to carve and then colour, then take a very light cut off the face so the colour is only in the carved bits. In both cases if you hollow out the bowl centre and maybe the edge of the rim after colouring you get nice crisp edges.
If you take a part-made item out of a lathe chuck it rarely goes back perfectly so its best to take the chuck off the lathe with the item in it. It gives you a handy holder for the carving process and depending on the design of the chuck you can often hold it in a normal bench vice. It can be put back on the lathe easily for finishing
Lime (Tilia, Linden etc) is favoured by carvers and does turn OK - not my favourite and it can be a bit dusty - but might be a good place to start.
You can borrow ideas from ceramics. Sgraffito is the technique of adding a glaze then cutting or marking through it before firing. Sometimes many layers of colour. Shapes can be more fluid than carving because there is no grain direction to worry about but many are geometric. A google (or search engine of choice) for Sgrafitto Ware images will bring you more ideas than you will make in several lifetimes.
Main thing - enjoy.
