Centering is one of the basic skills of throwing pottery on the wheel - first you work the clay off the wheel (wedge it) to make it as pliable as you wish, then you slam it down as close to center as possible and then you work the lump with the wheel turning to get it exactly centered.
The spout for a coil teapot can be made like they are for thrown pots or as you work your way up. The former method is to shape the spout as a hollow tapered cylinder, cut a hole in the body of the pot the size of the base, use clay slip as glue while you reach inside the pot and pinch the clay edges together and smooth them. In the latter case, when you reach the place where you want the spout to be, you either bend the ends of the coils out as you lay them down, or add coils that will run out the spout and attach them around a hole as you build up the body (sort of like ribbons attached to the hole or tentacles if the pot body is the octopus body) or add rings of coils from the hole, just like you were building a miniature body up sideways while you built the pot straight up.
In all cases, you probably have to make part of the spout with a tool inside to make the small diameter of the tip, unless you have very small fingers.
