Most modern glues are not able to re-bond to other glues or for that matter to themselves so clean timber to timber contact is a must, especially when working on the restoration of furniture.
Hide glue on the other hand will reglue to old hide glue and form a good strong bond to boot. This doesn't mean that you need not clean out the joint before reglueing, but you do not have to put in quite as much work as the old glue can be mostly removed with hot water and a rag without damage to the joint. The new glue will then bond to the residue that remains in the joint and is already keyed into the timber.
Hide glue comes in a pearl form and is mixed weight for weight with water. ie 100grams of pearls is mixed with 100grams of water. \This is left to soak for a short time, it will shell up during this time as the glue soaks up the water. It is then heated in a double boiler until it melts and kept at a constant temperature around 80ºC (women's leg wax warmers are perfect for this task). The glue should resemble a thick broth when it is ready for use.
Paint the glue on to both joints and press them together using a clamp. The new glue will melt the old remaining glue in the joint and form a new bond. You will have to work fairly quickly as the glue sets or rather jells very fast, especially in cold weather. The setting time can be retarded with the addition of a little extra water or by warming the joint prior to applying the glue.
Another plus for hide glue is its speed in setting. Because it works so fast it is some times not necessary to use clamps to hold a piece. In some instances you will find the addition of glue blocks to the back of a joint will strengthen and hold the piece together making for an easier and stronger repair.