PMD: Seventeen Plates DT 2

If talking about the latter, it works like this:
There are 7 (5 in later games) buildings in the Battle Frontier, each with their own set of rules. What doesn't change from building to building is that you need 7 victories to complete a tournament round. If you win 3 consecutive sets of 7 victories, you get to fight the building's champion, or Frontier Brain. These guys are harder than the League Champion himself, and get harder and smarter each time you fight them, sometimes adding tamed Legendaries in their teams.

If talking about the former, the PWT is a tournament hosted in a single building in which you get to fight every Gym Leader and every League Champion up to date, all mixed together. you start with the local ones at first, but the more you win, the more Gym Leaders you unlock. When you got them all, you unlock the Gym Leader Mixed Tournament (they all become as smart as Elite Four Members), and when you beat that 9 times, you get the Master Tournament, in which you get to fight all the Pokemon Champions.

That includes Trainer Red himself, and trust me, he's not easy. But neither are Blue/Green, Cynthia, Alder, Wallace, Lance, or any of the others. You only have to do 3 matches in total, but BY GOSH. WHAT MATCHES. In that mode, each of the three matches is the battle of your life. You never know if your team can counter what they have, or in what order they'll summon their 'Mons, nor which one they'll bring. And the remixes of their Champion Themes increases the drama so much.

Oh, forgot to mention: you fight a lot, so only 3 Pokemons allowed in both Battle Frontier and PWT. Beware of Red's Pikachu.

First off, the Elite Four. If you've indeed never played a Pokemon game before, they're basically the League Champion's personal bodyguards, and the representents of the league itself. After you get all 8 badges, you go to the League Plateau, finish the Victory Road, and upon reaching the plateau, you must defeat them all before fighting against the Champion and eventually get the title for yourself. They're essentially the BEST AI in the game, so even if you're overleveled, make one or two stupid mistakes with your team and they might destroy you.
What I'm trying to say with this is that the tournaments in the Pokemon games are ONLY for the Post Game Quests. You MUST defeat the League and finish the main story to unlock them, and it's better this way anyway, because you'd get destroyed if you tried to challenge them before that. They're extra challenges not relevant to the main story (and they're freakin' awesome, as well as really challenging).

In the Anime... First off, they ad MANY locations that are not in the game, and some of these locations have tournaments/competitions that happen randomly, so no, not like the game. As for the Elite Four, in the anime, you must complete a tournament with every other trainer that has collected 8 badges first. The winner (and the winner only) gets to challenge the Elite Four, and if he beats them all, the master. Which, as you've seen, never happens, which is why the Elite Four in the anime are usually represented as OP.
To be fair Ash should've been the winner in the Diamond & Pearl arc, but they threw this random trainer with a team of legendaries to prevent Ash from doing so, and thus to keep the series going the usual, STUPID way.

Putting that aside, Ash also fought against the Frontier Brains in the anime (after the League tournament), but even that was different, since he could fight them all instantly (with no tournaments before that).

Aaaaaaaand that's about it. Anymore questions?