Dragon tools are crafted using Dragon Ingots similar to vanilla tool recipes. The tools can be crafted once you have your first kill of any dragon.
You can imbue the tools with properties of the various dragons once you have learned the knowledge tome corresponding with each dragon type. To upgrade, interact with a Dragon Altar with the tool in hand.
If you somehow obtain an upgraded dragon tool that you have not killed the matching dragon, you will notice negative effects until you have proven your strength against that dragon.