As you cannot fly in Classic WoW, other than foot or mount, the main way to travel in Azeroth is through the use of flight points and ships. The Horde has its zeppelin network, and the Alliance also has an underground train running between Stormwind and Ironforge.
Flight points are taken through various Flight Masters, most of which are either Alliance or Horde. Alliance players cannot use Horde flight masters, and vice versa.To learn a flight master's available routes, you need to click on the flight master. Simply entering the area where the flight master lives isn't enough.
On the Alliance side, these are usually designated either Gryphon Masters or Hippogryph Masters (only in Kalimdor). On the Horde side, these are Wind Rider Masters and Bat Handlers (only in Eastern Kingdoms). There are two neutral flight masters in Ratchet, The Barrens and Marshal's Refuge, Un'goro Crater, and these can be used by either Alliance or Horde. These neutral flight points connect to the player's faction routes.
All Alliance or Horde flight points on a single continent connect to one another, although sometimes not directly. You may need to connect the flight through one or more other stops to get from one place to another. Flight points are only intra-continental. To cross to the other continent, you will need to use a Ship or Zeppelin.
Flights cost money; direct flights will cost less than those going through several other possible stops. Major cities act as "hubs" where flights tend to be the least costly. Direct flights are less expensive than routes that go through several stops. Depending on your financial situation, you may choose to stop at a flight further away from your destination based on the flight's cost.
One nice feature is Request Stop, a button that becomes available during a flight that allows you to tell the system to drop you off at the next flight point, not at the final destination. This only works if the flight has an intermediate flight point.
Differences from Retail: In Classic, there far fewer flight masters -- 34 Alliance, 31 Horde, including the two neutral flight points. For example, there are no Flight Masters in any of the 1-10 zones, few zones with multiple flight points for one side, and many intermediate flight points do not appear. If a flight path requires an unknown connecting flight point between your flight start and destination, you can't take that entire flight path until you learn the connection's flight point. In fact, it won't even show up as an option until you do
In Retail, there are about three times as many flight masters -- 95 Alliance, 90 Horde, including neutral flight points but not counting expansion-specific flight points like Azuremyst Isle, Ghostlands, Acherus, or Vash'jr. Most zones have multiple flight points within them. If a flight path has an unknown connecting flight point between your start and destination, it will fly you through anyway (though you won't be able to use "Request Stop" to land and learn the unknown flight point).
Here you can buy WOW Classic fly points for EU or US Servers.
You'll get guide for completing WOW Classic fly points