I'll tell a bit more about it, the how it was in Emerald and Platinum
In Emerald:The battle frontier is a facility that you unlock after beating the league for the first time. There are 7 different facilities. There's a Frontier Brain (like a gym leader) in each of them. Battle them once, you get a silver emblem and twice for a golden emblem (like a badge which is put on your frontier pass a sort of trainer card). Each time you complete a set of battle without losing, you get battle points (BP) that you can exchange for prizes (eg. Vitamins, dolls, held items, etc). There is two levels of challenge, Lv 50 and Lv 100. If you choose Lv50 and have pokemon above that level, they cannot be entered. Usually, 3 pokemon can enter the facility for a challenge. No items from your bag can be used, except if the facility includes it. Held items are usable, unless told otherwise and two pokemon or more cannot hold the same item. After each challenge, the next one will be slightly tougher.
- Battle Factory - you choose 3 pokemon from 6 suggested, all at the same level and with random items, moves, etc. You go into seven rooms where you are to challenge one trainer at a time with the chosen pokemon. Before entering a room, you are given a random hint about the trainer you're going to battle (eg. The trainer you're about to battle has a preference for water pokemon, or the trainer you're about to battle focuses on status inflicting moves). After each battle, your pokemon are fully healed and you are asked if you want to switch pokemon with one of the trainer you just battled. You only see the pokemon you want to have, neither it's held item, nor moves. If you reject the offer, you go on to the next room. You can retire any time from between battles. After going through 7 rooms 3 times without losing, you get to battle the Battle Factory Brain to get your silver emblem . After going through 7 rooms 7 times without losing in between, you get to battle the Brain again, and if you win, you get a gold emblem.
- Battle Pike - Here, there are again 7 rooms. You choose 3 of your own pokemon to go through that facility. When you go in, you see 3 doors, one left, one middle and one right. There is a lady there who gives you a hint of what awaits you in after one of the doors. For example, 'I have a feeling of nostalgia coming from the left door' will hint that there is a high chance that your pokemon will be inflicted by a status effect like poison, burn or paralysis. You get to the Pike Brain after going through the 7 rooms 3 times in a row (and if your pokemon are still able to fight
). The next time you encounter her, it'll be on the 7th time.
- Battle Castle - Here, you battle against 7 trainers again. This time, your pokemon will choose by itself a move, or stay there, loafing around, depending on how much you are close to your pokemon and its nature. After a 3 streak of 7 battles, you get to the Castle Brain for the first time, and on the 7th streak, you get him on the second time.
- Battle Pyramid - Here is another completely different facility. Your 3 pokemon cannot hold items. The pyramid consists of floors rather than rooms, which are a little like a maze. There, you are offered a special bag that you'll use to store the items you find on any floor. You can encounter pokemon on each floor. They can inflict status effects like poison or paralysis. You also have trainers (with 1 pokemon) on each floor which you may, or may not battle. When you enter the floor, you can only see one tile around you. After each battle you do, the visibility will increase a little. There is a warp tile to make you go to the next floor. After battling a trainer, you (s)he will tell you a hint (eg. 'the warp tile is towards left', or 'there are 2 items left on this floor') Once you got there 3 times in a row, through the multiple floors without losing the challenge, you get on to the Pyramid Brain. 7 times for the next challenge.
- Battle Dome - Here, you have like a tournament in which there are 16 participants. You can have a look at the pokemon of each participant, and a brief note about them. After choosing 3 pokemon, you get to choose 2 of them before each battle. After being champion of that tournament 5 times in a row, you get on to the Dome Brain. Then, on the 10th time, you get on him again for a rematch.
-Battle Arena - Take three pokemon with you. When a pokemon battles, there there will be only three turns, after which, if the neither pokemon fainted, the referees would declare one winner of the two by referring to three criterion; spirit (how many offensive moves the pokemon made), vitality (the pokemon with the more HP) and intelligence (the pokemon using the best moves). If there happen to be a draw, both pokemon faint, and if a pokemon fainted before the 3rd round, the battle continues, with the 'round counter' reset. 3 and 7 are the times in a row you have to challenge the Brain here.
- Battle Tower - Here, you are in a room where trainers come to challenge you, 7 in each challenge, all with 3 pokemon. Beat them all, 5 times in a row to get on to the Tower Brain, and 10 times for the rematch.
You earn more BP as you get more winning streaks (1st time, you can get 1, then 1, then 2, etc) in a facility and the Brain gives you a bonus of 10 BP.
In platinum:The battle frontier is again unlocked after beating the league for the first time. There are 5 different facilities. The Frontier Brain, the emblems, BP are again present The prizes however have changed (eg. Vitamins, scratch card, TMs). There only one level and pokemon will have their level temporarily reduced to Lv50 for nearly all facilities. Usually, 3 pokemon can enter the facility for a challenge. No items from your bag can be used, except if the facility includes it. Held items are usable, unless told otherwise and two pokemon or more cannot hold the same item. After each challenge, the next one will be slightly tougher.
There is again the Battle Factory and Battle Tower (both Brains appearing at 3rd and 7th won challenges in a row).
- Battle Hall - You take one pokemon and choose choose the pokemon type you want to battle with. Here, the level of your pokemon is kept. After you battled the chosen pokemon type, the level of that particular type will be raised a little (for a maximum of 10 times) [eg .chose fire at 1st level; battle charmander at Lv. 50, then chose fire at level 2, slugma is the random fire and is level 52... chose level 10 fire, Heatran Lv. 100]. When win 10 times in a row to win the challenge, and win challenges at 3 and 7 times to get on to the Brain.
- Battle Castle - Held items are not permitted here for you will have castle points which will be used here to exchange them for items and other facilities. Choose 3 pokemon and prepare yourself for 7 matches, without healing facility. You'll obtain castle points accoding to your performance, and the more you get, the more facilities you have. You can upgrade a facility with points, for example, you use 100 CP (castle points) to upgrade the healing of one pokemon to the restoring of HP of one pokemon or restoring of all PP of one pokemon, further upgrade restores both with less cost.
- Battle Arcade - Your three pokemon will have their levels reduced to level 50 temporarily. and held items are taken away for the duration of your challenge. The Battle Arcade is based on the luck of making a selection from a roulette board. You will be forced to try and select the square you want, which will determine what event will occur next. Depending on the event you may have a battle or even be able to skip it. Regardless, you will be coming back to the roulette board seven times a round to make a complete challenge. There comes again, the 3rd and 7th challenges in a row that will get your game on to the Brain.
Phew, that was long! If more details are required, just ask