Place the abstract painting on a piece of butcher paper. Use a marker to draw around the outline of the painting. Be careful not to get any ink on the frame or canvas.
Cut out the shape of your painting from the butcher paper and attach loops of blue painter's tape to the back; this tape can be removed easily from walls without damaging paint. Use this template to test potential locations for your abstract painting.
Choose the wall in the room that commands the most attention; this is most likely the wall that visitors' eyes are first drawn to. In a bedroom, this may be the wall behind the bed, while in the living room, the most noticeable spot may be on the wall behind the couch or fireplace.
Position the template on the wall you've chosen. Straighten it and step back to experience the full effect. Repeat until you've found a wall with which you're satisfied.
Arrange other pictures to complement the placement of the abstract painting once you've settled on a permanent spot. If the painting is small, don't place it alone on a large wall. If it's large, don't place other more normal pictures around it, as this will create a confusing aesthetic.