The process is fairly simple, but of course depends greatly on the original source, size, color depth, etc.
Will briefly summarize the few steps taken. Happen to be using Photoshop CS, but this approach certainly works for other versions, as well as other applications:
- Examine original file for dimensions and resolution. In the case of this original, the dimensions are 2592x1944 pixels, at a resolution of 72ppi (you wouldn't want to work at a lower resolution, typically). 2592x1944 translates to ~1.33:1, or a 4:3 aspect ratio. The desired resultant image is 1440x900, which translates to 1.6:1, or a 16:10 aspect ratio. Believe you can already see the discrepancy - the original image is "too tall" (read : too many vertical pixels) to be an instant translation to the newer pixel dimension.
- This would be where one needs to make a choice (and since I was deciding on your behalf, I chose both) : you can either resize to the maximum allowable dimension and add a matte, or you can choose to "lose" (crop) the pixels that are extraneous beyond the desired dimension. You could, of course, also resize the original to something less than the maximum allowable dimension as well, and add a matte on each of the four sides. Personal preference.
- Choice A : Resizing to the maximum allowable dimension with no cropped pixels. This choice will leave a certain degree of "space" around certan areas of the resultant image, which can be filled with whatever you might desire (I just made use of a black background, for simplicity). Open the original image, then select Image->Image Size. Under "Pixel Dimensions", adjust either the height or width to the maximum allowable, depending on your scenario (in this case, adjust the height to "990", as we have to "constrain" the height as too many vertical pixels exist). You will notice this changes the width to a value less than what is desired (again, in your case, to 1200).
- Choice B : Cropping pixels. This choice will remove the perhaps undesireable matte around the border; however, a few pixels will require sacraficing. Often, dependent upon the composition, they may hardly be missed. Open the original image, then select Image->Image Size. Under "Pixel Dimensions", adjust either the height or width to the maximum allowable, depending on your scenario (in this case, adjust the width to "1440"). You will notice this changes the height to a value greater than what is desired (again, in your case, to 1080).
- Create a new canvas to house the end result, with the appropriate settings - in your case, 1440x900 @ 72ppi, 8 bit RGB color depth. If you chose Choice A from above, you'll want to apply any changes to the background layer now (Layer->New Fill Layer->etc). Choice B requires no background formatting
- Simply copy the newly resized layer from the original from the layer window by dragging and dropping into the newly created canvas.
- Center the newly copied layer within the new canvas appropriately, using the move tool. Choice A should be fairly obvious that the height now matches the new canvas, and that it merely requires being centered horizontally. With choice B, merely center the layer horizontally, and then "eye" which pixels should be lost by finding the best composition of the pixels remaining (ie, move the layer until it "looks good"). As the canvas size is 1440x990, any extraenous pixels that exist outside the canvas area will automatically be cropped in a "Save As".
Am certain there are other ways to accomplish the same result.
Choice A v
Choice B.
(I happen to prefer B myself, but that is just my personal opinion)
Typically, whichever way functions for you and yields the desired end result is best.
Good luck.