Carpentry and Woodworking - Replacing Front Door Frame/Mouldings - Internal

I have to replace the inside moulding of my front door.
I purchased a prepackaged set with rosettes at the top and blocks at the bottom of the moulding. I have removed the old moulding.
Two problems: The door frame is not flush with the sheetrock/wall.
The new moulding is wider.
My Questions: How do the cut the base board to allow room for the new moulding. (I have hard wood floors) How do I attach the new mouldings? Thanks

The best way to cut the baseboard is to take it off. Take a utility knife and cut along the top edge between the basebaord and wall covering to free any paint or caulk. Carefully remove the baseboard and install your door molding. Fasten it with finishing nails. Set the nails below the surface with a nail set and fill the holes with wood putty and sand the holes. Cut your baseboard to length and re-install it.Prime and paint or stain.

If your door jambs are not flush with the drywall, you can fix it one of two ways. If the jambs are wider than the drywall, you must fill the gap at the outside of the moulding. Cut a thin strip of similar wood and attach to back of moulding. If the wall is wider than the jamb, do the same, attaching the strip to the inside edge of the jamb. Place a very thin line of caulk around the moulding to hide any gaps.