to start mining you will need a pickaxe
if you go to one of the place below you will see ore you can mine either in the walls or floor

Corundum Ore can be found at:

Greywater Grotto, South Southwest of Helgen (1 Ore)
Goldenrock mine at Darkwater Crossing, west of Mistwatch.
Halted Stream Camp, left of the Transmute Spell Tome.
Pinepeak Cavern, north of Ivarstead. (1 Ore)
Along the mountain edge north of Shor's Stone.
Eldergleam Sanctuary, on one of the edges
Broken Helm Hollow, east of Riften. when inside all to the back there's a chain pull it and there it is. 1 vein in main chamber.
Up in the mountains south of Hlaalu Farm and southeast of Brandy-Mug farm.
Northeast of Cragwallow Slope. At the mountainside on a rock underneath a pinetree.
Nchuand-Zel Excavation Site, in Markarth
Southeast of Windhelm, not too far from the gate.
Walking south (and a bit to the west) from Wreck of The Brinehammer will lead to two ores.
Pale Imperial Camp. The ore is a small distance to the northeast of the camp.
Southwest of Dustman's Cairn (Companion quest dungeon), when you reach the water head west along the shore, 1 vein.

Ebony Ore can be found at:

Redbelly Mine, directly west of Shor's Stone, and North of Riften
Mzulft, Southeast of Windhelm
Gloombound Mine, East of Windhelm
Throat of the World , Very top of the mountain

Iron Ore can be found at:

Embershard Mine, located southeast of Riverwood.
Half-Moon Mill, north of Falkreath
Left Hand Mine, just southeast of Markarth.
Fort Fellhammer, south of Dawnstar .
Rockwallow Mine, East of Morthal
Halted Stream Camp, north of Whiterun.
Northwind Mine, southeast of Mistwatch .
Iron-Breaker Mine, southeast in Dawnstar.
Saarthal
Whistling Mine, southeast of Winterhold.
2 veins south-west of Sarethi Farm.
Southeast of Hollyfrost Farm near Windhelm - another can be found going further south up in the mountains, the ore being east of an unmarked hunting camp.
Northwest of Narzulbur, behind some rocks.
Southeast of Cragwallow Slope.
Traitor's Post. Follow the road going southwest.
Souteast of Riverside Shack. South of Windhelm.
Not far north of Eldergleam Sanctuary.
A bit southwest of Rorikstead. Another can be found just north of Rorikstead.
South Cold Rock Pass. Just to the right of the cave intrance.
Bonestrewn Crest. One vein on the East side.

Moonstone Ore can be found at:

Mzulft, Southeast of Windhelm
Stony Creek Cave, Southeast of Windhelm
Soljund's Sinkhole, Southwest of Rorikstead
Cronvagnr Broodlair, in the Cronvagnr Cave

Orichalcum Ore can be found at:

Bilegulch Mine, Southwest of Fort Sungard
On the southwestern side of the mountain on which Bonestrewn Crest is situated.
Dushnikh mine, inside the orc stronghold Dushnikh Yal, southeast of Markarth.
Mor Khazgur mine, inside the orc stronghold Mor Khazgur, to the far north-west of Skyrim
Along the path to the Throat of the World
Along the road from Whistling Mine west towards Wintherhold. There ore is between some rocks a bit southwest from a unmarked hunting camp.
Atop a rocky hill, slightly south and due east from Dustman's Cairn, north-northeast of Redoran's Retreat.

Quicksilver Ore can be found at:

Quicksilver Mine, Northwest in Dawnstar
Purewater Run, West of Dushnikh Yal
Shrine of Azura, East of the shrine behind some snow banks.
Between Autumnwatch Tower and Arcwind point.

Silver Ore can be found at:

The Bloodlet Throne, past the throne room.
When coming out of Markarth, cross the East bridge (not the one to Left Hand Mine) and turn left up the hill
By Stendarr's Beacon east of Riften
Frostmere Crypt, just before Frostmere Depths
A small distance south from an unmarked hunting camp, south of Hollyfrost Farm near Windhelm
Along the path to the Throat of the World
Fenn's Gulch Mine in Karthwaster Northeast of the Lover's Stone

Malachite Ore can be found at:

The Throat of the World (Top)
Steamscorch Mine, directly North East of kynesgrove (There isn't a waypoint but you should see a door on the left of the pathway up the hill)

Gold Ore can be found at:

Kolskeggr Mine, South of the Lover Stone near Markarth
Lost Prospect Mine, East of Rifton North of the mountains. In the cave all the ore is located behind the waterfall.
Greywater Grotto, South south west of Helgen on the map.
Greenspring Hallow. To the southeast near the water.
Fort Neugrad. Access through the Prison basement, across lake to the left.

nearly all of this was taken from
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