The most important aspect of setting the print size for larger banners is resolution. What looks good on your screen at 8 by 10 inches and 72 pixels per inch is going to look awful at 8 by 10 feet. Banner placement is also important, and will help decide your resolution requirement. The output, or print size, is going to be 3 by 6 feet, but if you are not printing it yourself, you just have to consider the actual number of dots in your image. Also, if you are working in a photo editing program, converting the image from RGB to CMYK is important if it is not CMYK already.
Check the size and resolution of the image you will print to the banner. The total image size in pixels is the important number, such as 1,000 by 2,000 pixels. To find this information, right click on the image, then select "Properties" and then "Details." If the size is not specified, check the total image size in inches, and multiply that by the resolution to get the total pixels. If your image size is 3 by 6 inches, and the image resolution is 1,200 pixels per inch, your total image size is 3,600 by 7,200 pixels.
Divide the height and width of your image by 36 and 72, respectively, which is the banner size in inches, to get the dots per inch of your final image. Using our example, the image would print to the banner at a resolution of 100 pixels per inch, which is acceptable for a low-resolution image. To see how it would look in print, zoom in to 1200% on your screen. If you want a sharper image, you need more pixels, so either scan your image again at a higher resolution, or go to your image source for a higher resolution image. For very sharp images, at least 150 dpi is necessary, but remember that the banner will look sharper from a distance. You might not need the extra resolution.
Convert your image to CMYK in your photo editor to prepare it for print. If you are printing it yourself, send it to the printer and specify 36 by 72 inches in the print window that pops up. If you are sending it to a print shop, you just need to specify the size you want. The printer can take care of it from there.