You can visit the Blacksmith on most days from 9 AM to 4 PM. He is not open on Festival Days and I've noticed he is closed or leaves early on random days, not very often though. The shop is located to the southeast and can be accessed directly by the Mining Cart once opened.
Buying Ore
If you are not much of a Miner or you are just a few pieces of ore short, you can purchase it from Clint. If you need a lot it can cost quite a lot, but if you just need a piece or two it's not that bad.
Copper - 75g
Iron - 150g
Coal - 150g
Gold - 400g
Processing Geodes
When you explore down in the mines you will come across items that say "A blacksmith can break this open for you". DO NOT SELL THESE. Bring them to Clint and he can break them open for 25g each. A small price to pay for the materials that you will collect out of them. There are 4 different kinds of GEODES: Geode, Frozen Geode, Magma Geode, and Omni Geode. Each one will give you different materials. The Omni Geode gives the widest assortment. They will also give you coal and stone.
Upgrading Your Tools
Each of your main tools can be upgraded by supplying Clint with 5 bars of ore and a little monetary compensation. Upgrading your tools is vital to your day to day operations on around your farm and out in Stardew Valley. By upgrading your tools it will allow you to save stamina (as it decreases the number of hits required for rocks and trees and increases watering and tilling area) and gather other materials (stumps and large rocks). A gold pickaxe is required to break the meteorites (rare, but good source of Iridium Ore) that land on your farm.
It takes two in game days to complete the upgrade, and festival days do not count since he is not in his shop. You pick them up from Clint across the counter. You can't do any other interactions with him while he is upgrading your gear.
Copper Tool - Requires 5 Copper Bars and 2,000g
Steel Tool - Requires 5 Iron Bars and 5,000g
Gold Tool - Requires 5 Gold Bars and 10,000g
Iridium Tool - Requires 5 Iridium Bars and 25,000g
*The Blacksmith will be one of your most frequent stops. I like to have a chest specifically for my ores and geodes. I'll take my geodes once a week and break them all at once to help cut down on trips.