Putting a top sheet “upside down” is usually intentional, especially when the sheet has a printed or decorative side.
The trick is simple: place the finished or patterned side facing downward, toward your body. Then, when you fold the top portion of the sheet back over your blanket or comforter, the attractive side becomes visible instead of the plain underside.
That is one reason hotels and carefully made beds can look so polished. The folded section creates a neat decorative border near the pillows.
There is also a comfort benefit. On some sheets, the printed side feels slightly smoother or softer, so putting that side against your skin may feel better while sleeping.
A top sheet also acts as a washable barrier between your body and heavier bedding. Sweat, body oils, lotions, and skin cells collect on the sheet instead of directly on the comforter, which usually needs less frequent washing.
Of course, this does not matter much with plain sheets that look and feel the same on both sides. And plenty of people skip top sheets altogether.
So there is no strict “right” or “wrong” direction. But if your top sheet has a pattern, putting the decorative side down and folding it back is a clever way to make the bed look better while keeping the nicer surface against you.