I think you are confusing some terms from ESO with some other games.
To get blacksmithing ore, you don't need a pickaxe in ESO. you can just go to a mining node and interact with it to mine.
There is no mining trainer. There is a blacksmithing introduction quest (an ingame tutorial explaining how it works) in the first town you arrive in (Daggerfall city, vulkhel guard or davon's watch). Once done the tutorial/quest you don't have to interact with an npc ever again to make blacksmithing gear or level it up.
Through me you pass into the city of woe:
Through me you pass into eternal pain:
Through me among the people lost for aye.
Or just steal armor/weapons in town and deconstruct them at your nearest smithy. Just try not to get caught or else the guards will shake you down for gold and will take away any stolen items in your possession.
"Some enjoy bringing grief to others. They remind M'aiq of mudcrabs—horrible creatures, with no redeeming qualities."
Everyone knows the phenomenon of trying to hold your breath underwater - how at first it's alright and you can handle it, and then as it gets closer and closer to the time when you must breathe, how urgent the need becomes, the lust and the hunger to breathe. And then the panic sets in when you begin to think that you won't be able to breathe - and finally, when you take in air and the anxiety subsides...that's what it's like to be a vampire and need blood.
Francis Ford Coppola - BS Dracula: The Film and the Legend