There is an explanation of how to use a Battlesite in the Monumental rule book as well as on overpower.com, but I will go ahead and detail it here also.  There has been a change or two to Battlesite rules since the printing of the Monumental rule book, so anything on overpower.com that contradicts the rule book would be the official ruling.

    This next part is a very rare occasion but still rather complicated to explain.  The best way to explain it is to give an example first.  Let's say you have Beast on your team and you want to use Onslaught's Citadel as your Battlesite which has Dark Beast.  Since Dark Beast can play Beast Specials and Beast is on your team, you may still use Onslaught's Citadel as a Battlesite but you are not allowed to put ANY Beast Specials under the Battlesite.  These two characters are considered to be variants.  They are not the same character but have access to the same Specials.  Because one character on your team may play Beast Specials, you are not allowed to have any of his Specials under the Battlesite.  Even if you are not using certain Specials in your Draw Pile, you may not have any under the Battlesite.  Sorry if I sounded like I was being redundant, but it is rather difficult to explain.

    One major change that is not in the Monumental rule book is the One Per Code rule.  At first, players were allowed to use as many cards per character as they could fit under the Battlesite.  Unfortunately, it does not seem like this was play tested very much as it became rather frustrating for players to deal with so many avoids being used from the Battlesite.  Shortly after Locations were introduced, they added this One Per Code rule to Battlesites.  What this rule means is that you may only have one Special for each code.  This "code" is the two letters in the bottom left corner of the Special card.  This code helps classify each type of Special.  For example, the code AG is typically for all Special cards that read "Avoid 1 attack."  You may only have one of this code under the Battlesite, even if all six characters have one AG Special card available.  There are a few Special cards that are mis-coded, but those cards have little impact on the game.

    After you have picked the Specials you want to use for this Battlesite, you will need to add Activator cards to your Draw Pile.  Character cards are used as Activator cards, as there is no separate card called an Activator.  You will need one Activator card for each Special you place under the Battlesite.  If you have two Specials for a particular character, then you will need two character cards for that character to act as Activators.  If a character has a 3 stat version or has one or more clone characters, then these may be used as Activators in place of or in addition to the "normal" 4 stat character card.

    During the battle, when you want to play an Activator, you must choose one of your characters to play the Activator.  Even though the Specials are played because of the Battlesite, it is still your team that is playing the card(s).  Here is the Marvel recommended way to play an Activator:
    1)  Choose which character is playing the Activator by placing the Activator, face up, on top of the character [or in front of the character, or whatever can be consistent so that you and your opponent can easily know who is playing the Special].
    2)  Retrieve the Special from the Battlesite.
    3)  Play the Special as if it was played normally by the character who played the Activator.

    Most Special cards will have that character's name in the game text somewhere.  When playing cards from a Battlesite, replace this name with the name of the character on your team who is playing the Activator.