What exactly is a day bed, you ask? It's a twin bed disguised as a sofa by day and used as a bed at night. If your tiny space necessitates double duty for your bed, it's really quite simple to convert almost any twin bed into a day bed. Here are three pretty simple ways you can pimp out your twin bed into a multi-tasking day bed.
1. If you have a headboard and footboard, attach a piece or two of painted or stained wood running the length of one long side of the bed to make a sofa "back". It's easier to make up the bed if you attach slats rather than a solid piece of wood. Now you can add pillows all around the three closed in sides to make a comfy sofa-like seating area by day, throw off the throw pillows at night and sleep tight.
2. If you only have a headboard, push one long side up against the wall so the wall will act as the back of the sofa. Make or have an upholsterer make the angled bolsters like the ones in the photo. Even if you only have three sides to the bed decked out in these bolsters, it will give you the same effect. Of course you could still do this style if you have a headboard and a footboard.
3. The third option is to attach cushions or pillows directly to the wall behind the bed. You could sew ribbons on the pillows and hang them to fall at the right back height, or you could add snaps to pillows and attach a small fabric covered rail to the wall to which you've installed the other side of the snaps. There are many ways you could attach a cushioned section directly onto the wall along the long side of the bed.
The bed in the top photo looks 95% DIY-able. I think I could even make that.