Pinch the furniture at a place where the material is loose enough for you to pull it away from the cushioning and roll it between your fingers. Real leather will have a stiffness to it and stick to itself when it rubs together. Fake leather will feel thin and floppy, and you may notice the sensation of the textured underside grating together.
Search for a label that tells you what the furniture is made from, usually attached to the underside of the piece. This will inform you if the material is synthetic or real leather.
Smell the material. Leather has a distinctive smell that can't be imitated, whereas fake leathers will have a chemical smell. (A chemical smell doesn't necessarily mean fake, due to the scents of certain dyes and conditioners, but it's a decent indicator.)
Examine the edge and underside of the leather. Look for the end of the material; if it's fake, it will usually have a folded hem edge while real leather will simply have blunt, cut edges. You can usually find a fabric end on the underside of the bottom skirting portions or on the back of the piece of furniture.
Look at the pattern of the skin texturing on the material. On fake leather, this pattern is created using a machine or stamp and will have a repeating pattern, whereas the pattern of real leather has no repeating portions. You may have to look carefully and view a large area of pattern in order to see repeats -- though with some fake leathers, it will be pretty obvious.
Hold your hand firmly against the material for a few minutes. Real leather is porous, so your hand won't feel moist and sweaty or stick to it, though it will with fake leather.