Rub off as much of the adhesive as possible with your fingers. Weak adhesives will often ball-up into small clumps when rubbed.
Gently scrape off as much of the adhesive as possible with a dull knife or your fingernails, taking care not to scratch the wall paint.
Lubricate leftover adhesive with mineral oil, lard or another oily lubricant. Try to gently scrape off the adhesive again.
Use a strong solvent, such as paint remover. Keep in mind that strong solvents damage paint in addition to loosening adhesive. Also consider wearing protective gloves to prevent skin contact with the harsh chemicals in the solvent.
Sand off any leftover adhesive with sandpaper, but sandpaper will also remove the paint beneath the adhesive. Only use sandpaper as a last resort or if you are already planning to touch up or repaint the wall.