How do i get the .tga image on the right onto the mesh on the left?
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If you just want to make an object use your image texture, try creating a new material under your "Material Properties" tab, then choosing your image.
As long as you have unwrapped your Object, your image should be applied to the object. If it looks stretched, choppy or just tiled in a way you don't like; this is a reference to a node structure I use for my meshes.
But if you are planning on using images as like a background or even a wall, there is one option for you that I use pretty consistently and is built right into blender!
First thing you will want to do is go to your User Preferences under File -> User Preferences. next, go to the Add-On Tab in the middle and search for an Add-On called Images as Planes. Once you find it, click the little check box and close the User Interface window. Now, you can press Shift - A to add a new mesh as you normally would and instead of choosing a mesh, go to the bottom and select "Images as Planes". This will bring up a new window where you can choose your image file, and once it has been imported it will show up in your world as a plane.