1) Speak with Doric and ask him if you can use his Anvils. He will ask you to get him some materials first. Tell him that you will get the materials for him. He wants 6 clay, 4 copper ore, and 2 iron ore.
2) You can mine these items ahead of time and go ahead and complete the quest, but if you have not already mined these materials you can mine them almost anywhere, but I would suggest the Dwarven Mine located under Ice Mountain/ Falador since it’s the closest.
3) you have the materials, say that you have everything. Doric says he can spare some coin for our trouble and that we can now use his anvil any time we want. This will complete the quest and you are rewarded 1 quest point, 180 gp, and 1300 mining xp. You can now use Doric's workshop, as well as gain entrance to the Burthorpe mine (also requires level 65 mining).