The Gnomish Mines are an area for the game called
NetHack. You can access them from either
dungeon level 2, 3 or 4. Each
game, the downstairs will appear randomly on one of those levels.
I would recommend to enter those mines with at least 45HP unless you know what you do, there will be a flood of gnomes and dwarves that will try to take you down. Killing dwarves there is very good early on, you will be able to take their boots and cloak. If you are lucky, you might get a pickaxe, a shield or even a dwarvish mitril mail from them! The dwarvish mitril mail will protect as much as a plate mail, weights less and doesn't rust like a plate mail. If the dwarves are peaceful to you, you should bring in your pet and let it do the killing instead and then grab the loot. Remember that every dwarvish cloak worth at least 25 zorkmids so pick them up!
There is always a level that will be a kind of little town, most people refer to this place as Minetown. There is always an altar there with a priest, and there will be 3-4 shops also. One of the shop is always a lightning store where you will be able to buy candles that will be needed later on to complete the game. If the RNG is good with you, you might find a magic lamp that might give you one wish!
The mines are always ended with a special level, there is actually 2 variations of it. Each of the variation have something that you will look for: the luckstone.