I will have to move my Rhododendron in the Fall as it is too big for the garden it is in. What is the best way to transplant it. The new garden gets the more sun in the afternoon. Will that be a problem?
You don't say how established the Rhododendon is. The success of the move will depend somewhat on that - if it is only two or threes years old, you should manage. If it is 10 years old, you might have trouble. It is also advisable to root-prune the plant several months prior to the move. I'd recommend doing this in the fall, then moving the plant in the spring.
You have to dig as large a rootball as possible, then transplant just like you would any shrub. But you must make sure the roots are well-hydrated before you start and all through the process.
More sun usually means better blooms, so, yes, this is a consideration.
Here is a good discussion about moving trees and shrubs:
Finally, considering how problematic this move would be, especially if the plant is large and established, you should consider simply buying a new one.