Perhaps the easiest program to use is Photoshop Elements 13; it sports a new Facebook Cover option in the Editor's Create menu that makes a perfectly sized cover (and profile image) from one or more images using a variety of templates.
No matter which application you use, the first step is to create a new document at one of the sizes listed above, generally by choosing File > New and entering the correct dimensions and resolution (use 72ppi). Next, start importing imagery into your document and arrange the important bits so they're not covered by any overlays the service tacks on. To be safe, don't set any text inside the bottommost 145 pixels.
What to include
To make the best impression, use odd numbers of your very best images. Choose high-quality images that best reflect your personality or hobby. Use images you've shot yourself, purchased from a royalty-free stock image company, or those that are in the public domain or have generous usage rights (NASA's Visible Earth images, for example). But don't use images you've snatched from the Internet using a Google image search.
If it's a personal page, give your cover image extra personality by adding a favorite motto, such as "practice aloha" or "It's 5 o'clock somewhere!" Just keep it clean and keep it short. Remember, the whole world can see this, including current and future friends, family, mates, even bosses.
If it's a business page, be sure to include your URL and tagline so it's highly visible. If you have a product for sale, include a picture of it to increase brand recognition.
Save it in the right file format
When you're finished, first save a master copy of your document in the software's native format so you can edit it again later. Next, use the software's File > Save As command to create a JPEG or PNG copy in that you'll upload to the service itself.
The JPEG format produces a smaller file size, though PNG produces a higher-quality image because no data is lost when it's compressed. So if your cover image includes a logo or text, use PNG--8. If it includes a large gradient--a smooth transition from one color to another, like in a big sky--use PNG--24, which supports more colors than PNG--8 (and therefore creates a larger file size). For anything else, use JPEG at the highest quality setting.
Facebook is notorious for compressing JPEGs even further during the upload process, so if your cover image looks blurry, try PNG--8 or PNG--24 instead.
Keep these tips in mind, and your social media cover images will look their best and send the right message. Until next time, may the creative force be with you all!
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