Mining Levels 1-15:
You need a Bronze pickaxe. Your character should already have one form the start of the game. If not you can go to Lumbridge and talk to bob to go buy a new one for free. Now for this step you are going to want to mine all the copper and tine you can till you reach level 15. (F2P/P2P)
Mining Levels 15-30:
Form here you will want to mine Iron ore. This a great way to get some really fast levels in mining if. Now you can ether use this method to get up to 30 so you can mine coal or you can just power mine like a mad man and get to 99 form this method.
Where to mine Iron the fastest:
(F2P/P2P)Falador Mines: This spot is the best to mine iron or cause of how close the bank is also lots of iron down there. Also it is the fastest to bank iron if you have a dungeoneering level of 15. You may go to the Reasource Mine and bank there.
Mining Levels 30-70:
Now if you wish to spot power mining iron at level 30. Coal is a much faster way to get your Mining up. So now you will have to sit there and just mine all the way to 70 now if you wish to you can power mine this way to 99.
Where to mine Coal the fastest:
(F2P/P2P)Falador Reasoruce Dungeon: You will need a dugeoneering level of 15 to be able to use this method. This is by far the best method in both F2P and P2P. There is a great many ore veins at this location which make it good. Now for F2P player this will be a better slow method due to the high amount of people mining here.
(F2P/P2P)Mining guild: You will need to reach a mining level of 60 to use this method. Now this is by far the fastest method for free players. As you have 37 coal veins in the guild but you still have a lot of people but due to the high amount of veins it is faster than the Reasoruce Dungeon.
Mining Levels 70-99: Members only
Now for this method you will need to complete a quest line form the dwarves. But it is by far fastest method to get to 99 at this level. Here you will go mine a large amount of ether coal or gold form the Lava Flow Mines. This is the only place in Runescape where you can mine more the one coal ore or gold ore from a vein. This area is now the fastest place to level mining to 99. Now the best place to do this on is world 77 which is the home world for Lava Flow Mines.