If you download a certain type of aircraft, you usually get one airline livery with it. Wouldn't it be nice to have an aircraft in FS with your favorite livery? There are many repaints available on the known download websites, from various repainters and in various liveries. All repaint packages are designed for one uniqe aircraft, so you need to know exactly for what type of aircraft you want a new livery. Freeware developers like Project OpenSky and iFDG usually come with complete aircraft packages for each livery, so in that case you just have to install a new aircraft. But some of them come with the texture files only. If thats the case, you need to install the repaint into the folder of an aircraft you have allready installed. Be sure to download the right repaint package for the right aircraft. For the Project OpenSky Boeing 747 for example, there are a few different types: 747-200, 747-300 and the 747-400. So for a 747-300, you need to download a repaint for the 747-300 model only. Most aircraft also have different repaints for different engine versions, the most common are PW, GE and RR (Pratt and Whitney, General Electric and Rolls Royce).
Now lets say you download a repaint for the 747-400 in Qantas Livery with only the texture files. These packages are usually packed in a .zip file and should containt a folder "texture.(name of the livery)". Some don't have a texture folder, just the .bmp files. In that case, you need to create a texture folder yourself in the aircraft folder of the aircraft you've downloaded the repaint for. Most packages also contain a file with the aircraft lines you need to add to the aircraft.cfg of the aircraft you've downloaded the repaint for. It should be named something like "Add to aircraft.cfg", "[fltsim.x].txt", "Install.txt", "readme.txt", or something simular. In this file, you need to find a line that says "[fltsim.x]". If the package contains multible repaints, it may have lines like "[fltsim.x+1]", "[fltsim.x+2]", etc.
Now first unpack the .zip file that contains the repaint. Copy the folder "texture.(name of the livery)" (might be "texture.qantas" in this example) to the aircraft folder you've downloaded the repaint for (located in Flight Simulator 9/Aircraft/). In the unpacked .zip, open the file that contains the "[fltsim.x]" lines and copy those lines to the aircraft.cfg of the aircraft you've download the repaint for below the last "[fltsim.x]" that it is allready there.
Those lines may look like this:
[fltsim.x]
title=Project Opensky Qantas
sim=747-400-RR-RB-211-524HT
model=
panel=
sound=
texture=qantas
checklists=
atc_airline=Qantas
atc_flight_number=1234
ui_manufacturer=Project Opensky
ui_type=747-400
ui_variation=Qantas
visual_damage=1
atc_heavy=1
atc_id=VH-HFY
description=
Change "[fltsim.x]" to "[fltsim.1]". If there are allready multible repaints installed, you need to paste those lines below the last entry and increment the "x" of the new entry with one. So if the last entry is "[fltsim.3]", your new entry will start with "[fltsim.4]" and so on.
Make sure the "texture=" points to the folder that contains the new repaint. It might be "texture=qantas" in this case. Now the new repaint is installed and it should show up in the aircraft selection menu when you start FS the next time.
More detailed explanation of the [fltsim.x] lines:

(sorry the links above don't work, visit http://www.flightsimulatorguide.com/addons.htm for the original page)