Rotting Garage Door Frame

Remove the rotted boards fully, measure the needed lumber (take a piece to have to compare if it has a unique cut). Buy pressure treated wood and get a few scraps of slate tiles so you can prevent moisture from wicking up from the ground/concrete surface. Even still paint the wood ends before you nail it up. If it's not really replaceable get some rot penetrating protection to strengthen the wood and use polyester body filler to fill in the voids.

If you have a unique cut or molding you may need to find someone who can copy the pattern if the lumber yard don't offer it.