First obtain your piece of wood.
 
This is a pre-prepared "blank" of Oak which measures approx 3inches by 3 inches, It has already been cut to approximate shape and the end grain is coated with wax to prevent the wood from drying out too quickly and cracking.
 Next prepare the blank for mounting onto the lathe.
 
There are several ways of doing this depending on the size and weight and soundness of the wood and the intended final design etc.
 
Whichever method is used it is very important to ensure that the wood is securely attached. The lathe will be spinning the wood at around 850 rpm and it flies off it can hurt!
 
Here Ive drilled a hole in the middle of the blank on the end that Ive decided will eventually be the top of the bowl.
The blank has been screwed into a special screw chuck which is mounted onto the head stock of the lathe.
 
The head stock is always on the left side of the lathe and is the "active" end, powered by the motor to spin the wood.
 Vibration is a big problem when turning so here Im squaring the wood on the lathe to make sure that is perfectly round......
 ......and square.
 
Notice that the chisel or gouge is always resting on the tool rest. This ensured stability and stops the chisel being ripped out of my hands and really hurting!
Here Ive cut what will be the base of the bowl, made a depression, cut the circles that will eventually hold my name, date, etc and Ive marked the exact centre. The base has been sanded to final finish.
Now Im shaping the outside surface of the bowl from the base towards the top and always cutting away the wood "uphill".
 
Oak is hard and brittle wood so that the cuttings are more like chips rather than the long shavings that you get with other woods like Sycamore. Oak also has a distinct peperry tanin smell. Notice too on this photo and some of the later ones the grain pattern. Oak often shows medullary rays running at near right angles to the growth rings.
 The outside of the bowl is now shaped, although the foot will be cut and finshed later.
Ive now sanded the outside to final finish. Note the rather clumsy foot. Ive left it like this for the next step in the process, but it will be tidied up at the end.
The bowl is now reversed into the head stock chuck. The jaws of the chuck are gripping the foot and holding it perfectly aligned and securely.
So now I'm cutting away the wood in the middle, starting at the centre where the hole was drilled, and moving out to the edge.......
 ....as the bowl deepens
 The inner is now finished to final thickness......
 so that I can sand to finish.......
......before reversing the bowl again to finish the foot.
 
Here I've "jammed" the bowl between another piece of wood attached to headstock and the tailstock.
 
The tail stock has a pointed tip which is located in the dead centre of the base (that I marked earlier) to ensure that the bowl is centred and square.
 Im cutting away the wood at the foot....
 ...to complete the shape
 and finally the shaped bowl ready for decorating and finishing.
 
The whole process has taken a little over an hour to this point.