To install the trim, put a bead of sealant down the backs of the pieces and set them into place. Check for plumb and level. Hammer the trim into position with finish nails.It doesn't matter where you start installing the trim; just make sure it fits snugly before you nail or glue it into place.
Using paintable latex caulk, caulk the seams around all the trim (Image 1), and fill all holes and cracks with caulk.
After installing and caulking the trim, paint it with a semi-gloss paint made for kitchen or bath applications. Such paints hold up better in moist environments like garden windows.