Start with your horse safely tied.
Brush your horse’s back and girth area being careful to remove any dirt or grit that may cause chaffing under the saddle or girth. Brush so all the hair lies flat. Check the girth area as well, and brush or sponge away any dirt or mud. Leaving any grit on your horse's back or girth/cinch area can lead to painful galls, or irritations that can make your horse misbehave.
It is traditional to saddle from the near side (left side) but you should be able to saddle from the right (off side) if necessary.