Summarize:

Although each battle facility has its own set of rules, the following rules apply to all facilities: Eggs are not allowed. In addition, the following Legendary Pokemon are ineligible to participate Mewtwo, Mew, Lugia, Ho-Oh, Celebi, Kyogre, Groudon, Rayquaza, Jirachi and Deoxys. No duplicate items: Pokemon registered for a challenge cannot be holding two of the same item. For example, if you have a Pikachu and Electrike in your team, they both cannot be holding a Magnet. As long as this rule is observed, all items are allowed. No money or experience (Exp.) points will be awarded after a battle. Also, any Pokemon encountered in a facility will not be recorded in the Pokedex, even if you have never seen it before. The use of your Bag and any items included are prohibited during battle. Give your Pokemon any necessary items before beginning a challenge. Because the Battle Frontier is a dynamic area with different facilities and battling rules, you need to ensure that you have Pokemon specially trained for each facility. They need to have the proper Natures and moves, as well as any helpful Abilities. It is also advantageous to have your Pokemon EV trained. Find out more about EV training here: How to EV Train your Pokemon In order to face the Frontier Brain of a facility, you will need to achieve certain winning streaks. Depending on the facility, this may entail winning battles consecutively, or clearing a set amount of rooms or floors for each challenge. Because keeping a winning streak alive is a daunting task, it may take a while before you can encounter a Frontier Brain for either the Silver or Gold Symbol challenge. Don't give up! Should you earn all 7 Gold Symbols, your Trainer card will go up in rank. BP are awarded after each challenge, and the amount awarded will depend on the facility and how well you battle. These BP can be exchanged at the Exchange Service Corner for items, vitamins, or Secret Base decorations. Use your BP to purchase helpful items that will aid you in your challenges.
Know the Rules. Make sure your Pokemon are sufficiently prepared and trained. Persevere. Use your Battle Points (BP) wisely.