Buying aircraft can be done in four ways. Some are more convenient than others, but you'll find that buying aircraft in Airline Mogul is quite easy once you know the ways.
Buying New planes In-game
The In-game Aircraft Market is the place you'll spend a lot of time in. From here, you can buy brand-new airplanes directly from the manufacturer. It's a very easy way to buy new planes, but you will have to deal with the delivery times for each aircraft. Delivery times can vary from 24 game days for small airplanes, up to 268 days for large aircraft like the Boeing 747-400.
Choose the Aircraft
To buy a new plane, first you need to navigate to the Buy-Aircraft page. Go to Aircraft, and click View and Buy. On the left, you'll see a list of your current fleet. The right part, with the Purchase Aircraft header, is the part that matters here. You'll see a dropdown menu. In this menu, all the manufacturers that currently have planes available are listed. Select the manufacturer of the plane you want to buy, and click Select. You can also select All as manufacturer, that will show you all planes currently available.
After you've clicked Select, you'll see a list of all planes made by that manufacturer. Planes are sorted by name first, but you can sort using different data by clicking on anyone of the gray headers (for instance Seats). The different characteristics are explained here.
Once you've found the desired aircraft, click Buy behind that aircraft's data. This will navigate you to the next page, where you can select which engines you want.
Some planes have different choices of engines. This page will tell you if there are any choices, and will allow you to make the final decision. Once again, the page shows you the details of the airplane, but this time, watch out for any differences between various engines. Choose the airplane type you want by clicking the checkbox in front of the plane's data, then click Buy Plane.
Note that, even if there's only one engine choice available, you still have to check the box in order to be able to proceed.
Here, you can choose the number of aircraft you want to buy. Numbers can only be whole numbers, decimals are not allowed as that would make for a strange aircraft. Also, you can only order 99 aircraft at a time. You can enter the quantity in the bottom-right field that has the Select Quantity-header over it. Then, click Submit.
You'll see a list with the cost per plane, the total cost of your order, and the delivery time. If you want to change the quantity, you can do so the same way as stated above. If you want a different plane altogether, you have to start the process again. If you're happy the way it is, click Proceed to place your order. Once you've placed your order, you cannot cancel it. However, you can't order airplanes if you have insufficient cash.
Buying Used Planes In-game
Airline Mogul also has a used market, where airlines can sell their old or redundant airplanes. You can navigate there by going to Aircraft, and clicking Used Market. The Used Market lists all planes in two categories: Buy and Lease. Planes are sorted by name, but here too, you can sort by different data.
If you've found a plane you like, you can buy or lease it by clicking Buy next to the aircraft. The specified amount of money will be deducted from your bank account, and transferred to the original owner of the aircraft (this airline is listed on the used market too).
With used aircraft, you won't have to put up with a delivery time. However, the price of the aircraft may be up to 33% higher than the original price.
Buying Planes via the Forum
The Airline Mogul Forum has a section dedicated to buying and selling aircraft: the Aircraft Market. Here, you can view topics from other airlines asking for, or offering, aircraft, or you can create one yourself. Sooner or later, another airline will probably contact you to help you out.
Buying Planes from Official Brokers
Airline Mogul has four official brokers, all of which have their own thread in another section of the forum: the Brokers Market. You can view their prices, or negotiate your own, by replying in the thread or through any other means of communication. The brokers will take your orders, and supply you with the airplanes you want, for a lower price than normal. In some cases, you'll still have to wait for your planes to be delivered by the manufacturer.
Right now, you'll have to place your orders via direct communication, but a new brokerage system is in the making. It will make buying airplanes via brokers much easier and useful.