This is only the case where there is a very roughly equal amount of traffic from all directions and not a constant stream of traffic from one direction almost exclusively. In that case you can arrive from the minor road and if the traffic on the major road is constant it can be very hard to get out. This is often why they end up putting traffic lights in.
Wrong.
If everyone is doing it right you can turn as follows (I’m gonna have to reverse my normal instructions, as I drive on the left), including the changing lanes scenarioi:
Assuming a single lane approach with a dual lane on roundabout except where stated
- right (first exit) - stay in right lane. Always
- straight over (second exit) stay in right lane - but in a two lane approach there will be a two lane roundabout so you can approach in the left hand lane and use the LH lane on the roundabout and you exit in the left hand lane on the exit road. The exit road should have two lanes or if it is quickly a single lane road there should be width enough to merge with the right lane as you exit the roundabout. Always indicate right after you pass first exit. If going across in the right lane do not be the dickhead who objects to someone going straight across in the left lane, if they are forced to merge. If in the left lane, do not be the dickhead who carves up someone going straight across in the right lane if forced to merge.
So far - yes, stay in lane. Now it gets interesting
- turning left (third or later exit - yes some roundabouts have 5 or 6 roads converging). You always approach in the left hand lane if it’s a two lane approach. Go into the left hand lane on the roundabout (even if you enter from a single lane approach road). Indicate right ONLY after you have passed the exit before the one you plan to exit via - and at or after that exit you can (should!) move across from left lane to right lane so you are in the RH lane - the outer lane - at your exit.
For roundabouts with a 5th, 6th or even 7th exit (they exist) there is LOTS of on-roundabout lane crossing.
That’s when you change lanes on a roundabout. Here in UK our mother’s milk imbues us with the ability to adopt the same principles and enter in any of 4 approach lanes, navigate around a roundabout that also has four lanes and cross all of the lanes as needed, all without thinking. (Lots of lane and exit markings also helps!) And such large ones usually have entry traffic lights, too.
Think of the lanes less as concentric circles and more as outward expanding spirals which deploy centripetal force to spin you out at your desired exit. 
