Image Resolution

Generally speaking, the original file needs to be as close to the desired print size as possible when it’s at 300ppi.  

To check this, open the file in Photoshop (or similar editing software). Under Image Size make sure the Resample box is unchecked and adjust the resolution to 300ppi. The width and height listed in inches would be the optimum size for printing as long as the original file is clear.

To check if a file will print well at a desired size, even potentially larger than the “optimum” size noted above, you can also check the file in your editing software.

Use the crop tool to crop the file to the exact size being ordered at 300ppi. Then zoom in/out until the ruler reflects the accurate size of an inch in real life. What you see there should pretty accurately reflect the print's sharpness from an average viewing distance.

Notes:

Changing the resolution on a file does not affect the image quality. If you have a file that is 8×10 at 72ppi and you change the resolution so the file is 8×10 at 300ppi that will not add any quality to the file, the appearance will be the same.

There are various programs available that will use AI to add quality to a file, such as Topaz Gigapixel.