As mentioned in a previous entry on chivalric orders, members can display their decorations in their heraldic achievements.
Each order has it’s own rules on the display of the decorations but, they all have the same general guidelines. The lower level members typically have a decoration that is much like a military medal worn on the breast. These members can display the decoration suspended from the bottom of the shield, i.e. beneath the shield.
Higher level members may have what is termed a “breast star” that resembles (as the name implies) a large metal star with the insignia of the order. These breast stars are worn on the breast of the member and are much larger than the smaller medals worn by low level members. These individuals usually can display their decoration as well beneath their shield. (Below left: badge of the Most Venerable Order of St. John; Below right: Arms of Dr. Charles Drake, member of the Order)
The highest level members usually wear a decoration around the neck, much like an elaborate necklace or collar. These members can have that collar encircle their shield. (Below left: Collar of the Order of the Golden Fleece; Below right: Arms of HM the King of Spain)
As mentioned, these are the general rules of thumb but each order has it’s own specific rules. Sometimes, an order may explicitly state that another order (in general or specific) cannot be displayed with it. An example of such an order is the Légion d’honneur of France.
Also, there are orders that though they may have medals, ribbons and collars their members typically display their arms with something else. An example is the Order of the Garter whose members encircle their shield with the garter of the order. Though it is not unheard of to have both the garter and the collar, such as with the arms of John Churchill, 1st Duke of Marlborough.
Then again, there are orders that, depending on the level of the member (usually senior levels), have a symbol of the order (typically a cross) behind the shield. These are not to be confused with supporters which have a meaning unto themselves. Examples of these orders are the Order of Malta and the Equestrian Order of the Holy Sepulchre of Jerusalem.
If the member has more than one decoration, they can display them all under or around the shield, depending on the type. There isn’t any known restriction on the number of decorations to display, other than matters of taste.