On FSAirlines there are different ways to achieve new aircraft. This is what you will find when clicking on Buy/Lease Aircraft on the fleets page:
Get a brand new aircraft directly from the manufacturer. Only aircraft types which are still produced are listed here, but you can order as many as you want and they are instantly delivered.
This is usual the first place to look for new aircraft as you can pretty much always make a good deal on the traders list. Here you find aircraft which is sold by other airlines. The list is divided into public and private offers. Private offers can only be seen by your airline. You will notice that there are a lot of airplanes sold by FSA Aviation Inc..
If you don't have the money to buy an airplane then you can look for some great leasing deals here. When you click on the $-button you will first see the details about the leasing contract before you can accept the offer.
Aircraft orders (for out of production aircraft)
If you want aircraft which isn't produced anymore you can place an order here. But as these aircraft are harder to find it takes 1-5 days before your scout finds somebody who sells this aircraft. You will get a message when the aircraft arrives and then you have 1 month to buy it from the traders list.