When Ner'zhul recklessly opened multiple new portals on Draenor, the resulting magical stress tore the planet apart. The energies released in this catastrophe altered Deathwing's eggs, resulting in the nether drakes: ethereal dragons whose bodies are composed of energies from the Twisting Nether. Without Deathwing's guidance, these otherworldly nether drakes are just now finding their own way among the blasted ruins of Outland.

The nether drake information page has more details on the nether drakes themselves, including a movie.

Players earn reputation and complete quests for the Netherwing to earn experience, gold, and to ultimately receive a nether drake flying mount. This epic mount can best be described as "extremely cool." Once you reach exalted reputation with Netherwing, you receive a free nether drake mount after completing some quests. Additional nether drakes of different colors can thereafter be purchased for 200 gold each.

Every player begins at hated reputation. If you want to win over the Netherwing brood you will first need to talk to Mordenai, a NPC who travels around the Netherwing Fields in Shadowmoon Valley. He will offer you a questline that take you all the way to neutral reputation. Some of these quests require groups to complete.

To continue from neutral reputation, you need Artisan riding skill (300) which costs 5,000 gold to learn. You will not need an epic flying mount to continue on to Netherwing Ledge, but if you earned 5,000 gold for the skill, the extra 200 for the mount itself won't be that much harder to raise.

Once at neutral reputation, Mordenai will send you to the Netherwing Ledge after using the Dragonflight's magic to change your appearance to a fel orc riding a nether drake. Upon subsequent visits to Dragonmaw Fortress as well as Netherwing Ledge, you will automatically be transformed back into this guise when near either of those locations. While in disguise, most orcs in the region will consider you friendly and not attack on sight - with the exception of Dragonmaw Ascendants, Dragonmaw Skybreakers, and Dragonmaw Transporters. The Ascendants are especially deadly since they are elite monsters and can make quick work of players.

Neutral -> Friendly

Once you reach neutral you have access to several one-time quests and daily quests which are available at the Dragonmaw camp on Netherwing Ledge.

Miners, herb gatherers, and skinners can do daily gathering quests in the area. If you don't have any of those skills, you will not be able to do these quests, even if you end up finding the materials. But don't worry; there are plenty of other quests to do.
Netherwing Crystals (Daily) - This daily quest requires you to gather Netherwing Crystals, which drop off monsters in the area. You can combine this quest with some of the other daily quests for greater efficiency. Crystals drop off some monsters more than others, so try to find out which monsters drop them most often.
A Slow Death (Daily) - This daily quest requires you to gather Fel Glands from various monsters and use them to poison Dragonmaw Peon camps. This quest can be completed while in a group, where the entire group can gather fel glands then complete the quest together. Make sure the entire group is close to the peon camps when poisoning them. This quest might seem to take a long time until you learn which monsters drop the fel glands more often.
The Not-So-Friendly Skies (Daily) - This daily quest requires you to collect Netherwing Relics, which drop from the Dragonmaw Transporters that fly overhead. To attack them, you can land on one of several floating islands around Netherwing Ledge and hit them with a ranged attack as they fly by. The islands can support several players at once. There are other areas where you can intercept the transporters as well, such as a spot near the landing pad on Netherwing Ledge next to the two giant Ascendants.

The Great Netherwing Egg Hunt - Netherwing eggs are scattered throughout the Netherwing Ledge and Dragonmaw Fortress vicinity, and are quite rare. This quest only requires turning in one egg, but it can be indefinitely repeated for extra reputation. Besides finding them on the ground, you can also find them as drops from nearby monsters or while using gathering tradeskills on nodes in the area. Netherwing eggs are a great way to earn reputation after you've completed all the daily quests you wanted to do for the day.

Friendly -> Honored

Once you reach friendly, you will have more quests and daily quests available to you. You can continue to do the previous daily quests in addition to these new ones, since they will continue to be a source of reputation gain and money rewards.

Picking Up the Pieces (Daily) - This daily quest, which takes place in the Netherwing Mines, requires you to recover 15 Nethermine Cargo. You can find them spread throughout the mines, and you might stumble on some Netherwing eggs while you're there if you're lucky.
Dragons are the Least of Our Problems (Daily) - In this daily quest, you are asked to slay 15 Nethermine Flayers and 5 Nethermine Ravagers. The Flayers are easy to find while the Ravagers are a bit rarer. Keep an eye out for them as they patrol around the mine - if you see one, attack it quickly. These monsters also drop Netherwing Crystals which can be used in one of the quests listed above. While doing this quest, you can also find Netherwing Eggs, Nethermine Cargo, and mining nodes for other turn-ins.