Attach matching headboards to the head and foot of a twin bed frame. These will become the sides of the day bed.
Cover the mattress in a sturdy fabric. A quilted fabric is a good choice, as it's comfortable to sit on, padded and long-wearing.
Add pillows. Because a twin mattress is wider than a couch and therefore not so comfortable to sit on in the usual way, you can add long, thick, firm bolsters along one side of the mattress, propped against the wall behind, with additional pillows in front of them. But this is not necessary. Simply adding bolsters or pillows at the ends, next to the headboards, will achieve a stylish look and be comfortable for lounging.