To get the ability to craft one Franklin's inventions, you must collect his almanac pages and you will get the "recipes" for them. You then must have the supplies and the correct "craftsman" for the job. It's best to attempt this achievement after you have completed all Homestead missions so that everyone is leveled up and you have access to all supplies. After doing all of this, you just have to use the Accounting Book. Inside the front door the the manor, look left and you'll see a book in a room that lets you craft. These books are also in all of the general shops.
Note: You must craft all of his recipes anyways for the 100% DNA Tracker.