RULE SUMMARY
The Pokemon TCG is a very simple TCG, all things consisdered. Each player has a deck of 60 cards, no more and no less. You can only have four cards inm your deck of the same name, with the exemption of basic energy. First thing anyone does is flipping a coin, each player gets to choose a side and whatever side wins gets to choose who goes first. after that, each player draws seven cards. Using the cards in this hand, both players put down as many basic Pokemon as they wish (anything more than one is optional). If they do not have basic Pokemon, they shuffle their deck and draw a new hand of seven. For each time a player does this, the other player may draw an additional card, and if it is a basic it may be played. After this, both players put six prize cards into play, and turn one begins. During the first turn, the player who goes first cannot attack or use a supporter card.
Pokemon themselves are rather simple. You can play a basic from your hand during any point in your turn, and you can evolve any basic into a stage one or stage 2 the turn after they are put into play. You can attach energy to Pokemon (once per turn), which is used to attack. Using an attack ends your turn, but if a Pokemon has an ability, they can use it and it won't end your turn. If you knock out an opponent's Pokemon, you take as many prize cards as the card says (1 for most cards, 2 for EX/GX/V, and 3 for Tag Teams). Your bench can have five Pokemon by default.
Trainer cards are a bit more complex, but not really. There are four types of trainer cards. Item cards are the most simple, there are no rules attached. Tool cards, which are technically a subset of items, can be attacked to a Pokemon in order to give them a buff of some sort. Stadiums affect both players and remain until someone plays a new one. Supporters have big effects, but only one can be used per turn.
The discard pile is where cards go when their effect has worn off, such as a KOed Pokemon, a trainer after being used, or a discarded energy. Unless a card mentions it, you can not get those cards back.
There are two major formats in the Pokemon TCG, Standard and Expanded. Standard has consistent rotations at the end of August, usually getting rid of four sets. Currently, Standard is Ultra-Prism onward, but will likely rotate to Tag Team onward. Expanded seems to be unchanging, aside from a few banned cards every card from Black and White onwards is legal. There are a few types of cards with gimmicks of sorts.
EXes: an Expanded only type of card. They give up two prizes, in exchange for (what used to be) much stronger attacks. Power creep has not been kind to them, and only a few still see play
Megas: another Expanded only type of card. They are played onto an EX they evolve from (Blastoise EX ---> Mega Blastoise EX), and unless you have the corresponding spirit link it ends your turn. They give up two prizes, and once again were highly power-crept.
Ancient Traits: otherwise standard cards, they have a bonus. Things that delete abilities don't touch them
BREAKS: An additional evolution to Pokemon who don't usually evolve, they have a new attack or ability but don't effect pre-existing ones
GXes: The first of these cards still legal in standard. Somewhat akin to EXes, they have stronger attacks and give up two prizes. Unlike them, you must evolve up to use them (You play Gardevoir EX as a basic, but Gardevoir GX must evolve from Kirlia) and have a special, once per game GX attack.
Prism Stars: One prize Pokemon with gimmicky effects. You may only have one of each Prism star in your deck, and instead of going to the discard pile they go to the Lost Zone, completely unobtanible
Tag Teams: Even stronger GXes, that give up three prizes.
Vs: Literally just EXes
Summary of the current metagame
(I play mostly in Expanded, so that's what I'm going over here. If you want a summary of the Standard format, watch PTCGradio, his videos are quite informative.)
Most people play a roughly 10/40/10 split of Pokemon/Trainer/Energy, but it varies based on the deck. Various staple cards include...
Professor Juniper/Professor Sycamore/Professor's Research: Discard your hand, draw seven. One of the best supporters in the game, practically a four of in every deck.
Cynthia (SM: Ultra Prism): Shuffle hand into deck, draw six. Another great supporter, better for more safe players who don't want to throw away all your cards.
Lysandre (XY:Flashfire): Switch your opponent's active Pokemon with one of your choosing. Good for taking out a Pokemon your opponent is setting up.
Guzma (SM: Burning Shadows): Switch you and your opponent's active with one of your choosing. Despite the similarity to Lysandre, both coexist rather well, most use one of both.
Welder (SM: Unbroken Bonds): Attach two fire energy in your hand to any of your Pokemon in play and draw three cards. It lets you put three energy into play per turn, which speeds thing up significantly. Any decks that use fire energy or don't care which energy they use use it.
VS Seeker (XY: Phantom Forces): put a supporter card in your discord pile into your hand.
there are way more, but I'll go into more detail later. I spent an hour writing this, I'm tired.