The short answer.
3840 × 2160 pixels, 16:9. That is the size of the Frame's own screen, so art made at that size fills it edge to edge with no border and nothing cropped.
Anything smaller gets stretched to fit and goes soft. Anything another shape gets a border or a crop.
Why the shape matters as much as the size
The Frame is 16:9, the same shape as most TVs and computer screens. A photo from your phone is tall, and a print scanned from a frame is often closer to square. On the Frame those will not fill the screen exactly.
Stretching a small picture up to 4K does not add detail. It only makes the soft parts bigger. If you want it sharp, start with a file that is already 3840 × 2160.
How to check a file before you load it
On a Mac. Click the file once, press Command and I, and look under More Info for Dimensions.
On Windows. Right-click the file, choose Properties, then Details, and look for Dimensions.
You want to see 3840 × 2160. If it says 1920 × 1080, it is a quarter of the detail.
Mats, brightness and colour
The Frame can put a mat around a picture, the border you would see in a gallery frame. You pick a mat style, then a colour, with Left and Right on your remote, if you like that look.
In the SmartThings app, Art Mode settings has Brightness and Color tone. The Frame also adjusts to the light in the room on its own. Keep it low in the evening so it reads like a painting, not a screen.
Getting it onto the Frame
Two ways: a USB stick, or the SmartThings app on your phone. Both are written out step by step on my Samsung Frame guide.
Art made at that size
Every piece I make is 3840 × 2160 PNG, 16:9. Every collection is signed, comes with a certificate and the story behind it, and downloads the moment you pay. The files are yours. Put them on every screen you own.