Step 1
Talk to Doric.
Collect 6 clay, 4 copper, 2 iron ores.
Talk to Doric again.

Items needed: 6 Clay Ores, 4 Copper Ores, and 2 Iron Ores to speed things up.

Head over to Doric in his little house north of Falador. He will tell you that before he will let you use his anvils, you must bring him more supplies since he is running out. He will ask you for 6 clay ores, 4 copper ores and 2 iron ores. He will give you a bronze pickaxe.

You must either mine, buy, or find the requested ores. If your Mining is below 15 you can still buy the iron ores, and mine the rest. The nearest clay/iron/copper mine is the Dwarven Mine, located north of Falador. Collect the ores and return. They must be un-noted.

Doric will be very pleased when you talk to him while holding the ores. Simply talking with him will give them to him. He will reward and thank you.