Download the following addon: Gathermate2
This addon shows you every Mining node location on your map. The addon and the databse can be found here.
Don't forget to turn on Find Minerals!
Check out my Smelting guide 1-600 if you want to level mining with [Smelting] only. You can level mining a lot faster with Smelting, but it will also cost you a lot of gold. (you can make most of your gold back if you sell the bars at the Auction House)
You can now mine ores without a required skill. The amount of ore you'll get is determined by your skill level. But this means it's still recommended to level in zones where your skill level is close to the mining deposit hidden skill requirement. You will get much fewer ores if you start picking the highest level ore with mining skill 1. You can read more about this here.
I don't recommend mining ores at Draenor if you want to level mining fast. You can't use flying mount at Draenor, so you will level a lot slower there. (disregard this if you have the flying mount achievement)

1 - 50You should always smelt your ores to gain a few free skill-ups, the only exception is if you need the Ores for Jewelcrafting.
You will mine [Copper Ore] in this section.
Durotar
Darkshore


50 - 100Learn Mining Journeyman.
You will mine the following ores: [Tin Ore], [Silver Ore]
Hillsbrad FoothillsHillsbrad Foothills is just simply the best place to farm Tin. If you are an alliance player you should still go there, but Northern Stranglethorn is a great alternative. You will see a red zone on the map, that zone is filled with Tin, it's everywhere. When you mined all of it, just go outside of the zone where you can see the little yellowish arrows, mine a few Tin and head back to the red zone because it's most likely that the Tin Veins there are already respawned.
Northern Stranglethorn

100 - 150You will mine the following ores at this section:
[Iron Ore], [Gold Ore]
Western Plaguelands
Feralas


150 - 200Learn Mining Expert.
You will mine the following ores: [Mithril Ore], [Truesilver Ore]
Felwood and Burning Steppes are the best places to farm because the mining route is just so simple in these two zones. Badlands is also a really good place, but I found a bit more Mithril in the other zones.
Felwood
Burning SteppesDon't go into Dreadmaul Rock. There is plenty of Mithril at the corner of the map, you will just get dismounted if you go into the cave and it will slow you down.
Alternative Map: Mithril Ore farming

200 - 300Note: There is currently a bug for some players where you won't get any skill points for mining Rich Thorium Veins even if it's orange to you. If this is the case, your only option is to smelt Thorium up to around 275 then head over to Outland after you reach level 58. If you are already above level 58, then you can just go to Outland and mine Fel Iron Ore.
Learn Mining Artisan.
You will mine [Thorium Ore].
Un'Goro CraterWinterspring


Alternative Maps: Thorium Ore farming

300 - 325You can also just skip this part entirely and start farming Cobalt Ore.
Visit your trainer and learn Mining Master.
You will mine [Fel Iron Ore]. You can stay in this zone up to 350.
Hellfire Peninsula

325 - 350You will mine [Adamantite Ore] and [Fel Iron Ore].
Zangarmarsh

350 - 400Visit your trainer and learn Mining Grand Master.
You will mine [Cobalt Ore]. I found Howling Fjord to be the best place to farm Cobalt, however you can go to Borean Tundra if you want to, there are plenty of Cobalt there too. Visit my Cobalt Ore farming guide if you want to go to Borean Tundra.
Howling FjordAlternative map: Cobalt Ore farming

400 - 425You will mine [Saronite Ore]. Sholazar Basin is simply the best place to farm Saronite.
Sholazar BasinWintergraspAttention! Currently it seems that sometimes there is a bug and you can't see any mining nodes, or even npcs in the zone. Logging out and then logging back in fixed this bug for me, but you might even have to close the game.

425 - 475Learn Mining Illustrious
You will mine [Obsidium Ore].There is a lot more Obsidium in Hyjal than in Vashj'ir, but there is also a lot more players. Hyjal beats Vashj'ir if there isn't anyone else farming the zone, else the zones are pretty similar. If you go to Vashj'ir, you will also have to do the starting quests until you get your underwater mount.
Mount HyjalVashj'ir Mining Map
475 - 500You will mine [Elementium Ore].
Twilight HighlandsYou can also just skip this part entirely and start farming Ghost Iron Ore.
Alternative map: Elementium Ore farming.

500 - 600The last 10 points will come really slowly. Visit my Ghost Iron Ore farming guide if you need more farming places.
Ghost Iron is green all the way up to 600, but if it's gray to you, it's because you have a mining pick in your inventory, or something that gives you extra mining skill. Don't worry, you will still gain skill-ups, even if it's grey.
Jade Forest
600 - 700You can learn the new rank of mining from [A Treatise on Mining in Draenor]. You can get this scroll by mining Blackrock Ore or True Iron Ore at Draenor.
Frostfire RidgeShadowmoon Valley
700 - 800You can get the next rank of Mining by simply mining any ore at one of the Broken Isle zones.
In Legion, there are new types of mining nodes, Leystone Seam and Felslate Seam. You can only find these in rivers or in caves. The farming route below is optimizted for finding these nodes because the basics Leystone Depost and Felslate are only good until around 730, then you have to find Rich and Seam nodes to reach 770. And at around 770, even the rich nodes are grey so your only option is the Seam nodes found in caves and rivers.
Important! 785-800 will be the hardest part because the only node that will give you mining skill is Felslate Seam, which is a rare spawn of Leystone Seam. And for the last 5 points you can only get skill points for mining [Infernal Brimstone] world quest. It's one guaranteed skill points every 2-3 days when the World Quest pops up. Always check every zone, and look for little mining pick icons, you will see which one awards Infernal Brimstone if you hover over the icon.
Unlocking World QuestsComplete Uniting the Isles by reaching friendly reputation with every Legion faction. You can get this quest from Archmage Khadgar.
After you unlocked the quests, you have to level your Mining to at least 100 to unlock the profession World quests.
Darkmoon FaireYou should check your Calendar in-game to see if the Darkmoon Faire is open, the event starts at 00:01 on the Sunday before the 1st Monday of each month.
You can gain +5 skill points by completing a single quest (use it at 795). Click here to read more about the quests.

SuramarSuramar is a level 110 only zone.
If no one is farming the ores befoure you, these 5 caves should always have 1 seam node and one normal node. Mine out every Seam you see, even if it's a grey Leystone Seam, it can respawn as Felslate Seam.
Go inside the cave and walk to the end because you often don't see the ores on your minimap from the entrance!
Coordinates if you have TomTom addon: (just type these into the chat)
/way Suramar 40.4, 29.4
/way Suramar 31.5, 26.1
/way Suramar 24.2, 50.7
/way Suramar 28.3, 56.2
/way Suramar 29.3, 50.8
You can turn off [Mana Divining Stone] by right clicking on the buff. I usually turn it off because it's really annoying while farming.