Without legal restrictions, Pokémon Battling is basically pitting 6 of your own Pokémon against 6 of your opponent's Pokémon over a link cable. Level 100 is the highest you can go, so it's best to train your Pokémon to level 100. Use your best Pokémon! It's recommended that two of the same type of Pokémon is not a good idea, but if you think that it gives you an advantage, do so! First, we will talk about the two commands to battle. If you have battled many times before, you can skip this section.
Attack: This is where you attack the enemy. Choose one move from a movepool of up to four moves, and you will attack your opponent with that move. Depending on the move you have chosen, it could hit or miss, not attack right away, or not have any obvious or immediate effect.
Change: If you want to exchange Pokémon, simply go to Change and choose a Pokémon from your party of up to six Pokémon. Note that when you switch, your opponent's selected move (this is turn-based, after all) will strike while your action is switching, so make sure that you don't make a bad switch.
Now, onto the stats of each Pokémon. There are six in total: HP, Attack, Defense, Special Attack, Special Defense, and Speed. Pokémon attacks are split into three types: Physical, Special, and ???. Seriously, Nintendo classifies the third type as ???. For the sake of simplicity, we will only focus on the first two types. In the 1st, 2nd, and 3rd generations, the damaging moves that deal physical damage are Normal-, Fighting-, Poison-, Ground-, Flying-, Bug-, Rock-, Ghost-, and Steel-types. In the 4th generation, a physical attack is one in which your Pokémon directly attacks the opponent with claws, teeth, etc. The amount of damage done by physical moves is determined by a) the power of the attack, b) your Attack stat, and c) your opponent's Defense stat. How much damage you take from a Physical move is determined by your Defense stat and your opponent's attack stat. So far simple, right? If you have a low Attack, then you will have trouble dealing a lot of damage with Physical moves; if you have a low Defense, you will have trouble surviving Physical moves; and vice-versa. The other type (besides Physical) is Special. The damaging moves that deal Special damage, are Fire, Water, Electric, Grass, Ice, Psychic, Dragon, and Dark, (in generations 1-3). In Generation 4. a special attack is one in which an opponent is struck by a beam of light, etc. The damage dealt by a special attack is determined by a) the power of the attack, b) your Special Attack stat, and c) your opponent's Special Defense stat. How much damage you take from Special move is determined by your Special Defense stat and your opponent's Special Attack stat. Again, very simple. We now take the Pokémon Alakazam as an example. Alakazam has a very low Attack and very high Special Attack. With the information that you were provided above, it is best to give Alakazam a Special attack, such a Confusion (type: Psychic), rather than giving it a Physical attack, such a Dig (type: Ground). Now, you know to find Special Attacks for Alakazam and not Physical Attacks.
"The power of the attack" was mentioned earlier, so what is it? An attack has four characteristics: a) power, b) accuracy, c) type, and d) special effects. Let's take the move Ice Punch. Ice Punch's characteristics are a) 75 base power, b) 100% accuracy, c) type: Ice, and d) has a 10% change of inflicting the status Freeze to the opponent. Now, what does 75 base power mean? For a rough explanation, base power shows the strength of an attack originally. Once again, let's take Alazakam as an example. Mega Punch (type: Normal) has a base power of 85. However, if you look at your Alakazam's stats, you will once again see that its Special Attack is most likely more than double its Attack. In this case, even though Mega Punch has a higher base power than Ice Punch, it is a Physical Attack so it will deal less damage than Ice Punch if Alakazam uses it.
"Base power" was mentioned earlier, so what is it? Base power is the power that is officially given to us. Several things can change this. First, there is something called Same Type Attack Bonus, or in short, STAB. If the type of the move you are uses matches at least on of the types of the Pokémon using it, then the attack receives a 1.5x move bonus. Confusion's base power is 50, but if used by Alakazam (Confusion's type is Psychic, Alakazam's type is Psychic), then Confusion's power will be: 50 x 1.5 = 75 power. Second, there are Type Alignment Advantages. Third, there moves that temporarily raise a type's power. Fourth, there are items that temporarily raise a type's power when attached. And finally, there are Abilities that raises a type's power under special conditions. These will be discussed later.
Attack, Defense, Special Attack, and Special Defense have been reviewed. Now, it's time for Speed. Speed is not complicated at all, since for most cases, the Pokémon with the higher Speed moves first. In case of a tie, it will be a coin flip. In Red, Blue, Green, and Yellow versions, Speed is a major contribution to Critical Hits. A Critical Hit is simply a chance that your attack will hit a gap in your opponent's defenses and deal double the damage that it was supposed to do. The higher the Pokémon's Speed, the more chance it has of dealing double damage. Note that this only applies to the First Generation.
Finally, there is HP. HP stands for Hit Points, or Health Points. With either interpretation, if your HP reaches 0, then your Pokémon will faint. This means that you must switch out this Pokémon without the penalty of your opponent having an extra move, and that this Pokémon cannot fight in the same battle again unless an item is used to revive it. Note that for player(s) vs. player(s) battles, item usage are not allowed but attached items can be allowed. As you get hit, you lose HP, but there are moves and items that can raise your HP back up again. We will talk about this later. The point is, if you think that your almost-fainted Pokémon will be of some use later, switch it out so that it won't faint.
While Pokémon stats are talked about, we need to remember that they are quite random. If then, how is Zapdos' Attack compared to someone else's? There is a system called Base Stats. Base Stats are values used to compare stats more easily. For example, your level 10 Charmander might have a higher Attack than a level 10 Bulbasaur, but a level 10 Charmander could, in theory, have a lower Attack than Bulbasaur. When base stats are checked, Charmander's Base Attack stat could be 52, and Bulbasaur's Base Attack stat could be 49. This means that most of the time, Charmander will have a higher Attack than Bulbasaur, but not all of the time, since Bulbasaur might use a move or item to raise its Attack stat. Another use is to compare stats within a Pokémon. Alakazam's Base Attack stat is 50, and its Base Special Attack stat is 135. What this means is that even if Alakazam uses a Physical Attack that has double the power of a Special attack, the Special attack would still deal more damage because Alakazam's Base Special Attack stat is more than twice its Base Attack stat. Yes, Fire Punch (damage: 75) will deal more damage than Hyper Beam (damage: 150) coming from Alakazam. I cannot list the system because every Pokémon has 6 Base Stats for HP, Attack, Defense, Special Attack, Special Defense, and Speed. Almost every Pokédex out there has base stats for each Pokémon, though.
While the subject is being discussed, it is important to keep an eye on your move's Power Points (PP). Every move has PPs that determine how many times you can use that move. When a move's PP reaches zero, you cannot use that move anymore. When all four of your moves' PPs reach zero, then you will use a move called Struggle, a low-damage move that will hit all Pokémon. You will even take damage from this move yourself.
Items cannot be used during a player(s) vs. player(s) battle, but one item can be held by each Pokémon. The item can either be a one-time usage (or two, but we will get to this later) or permanent. After the battle, your one-time usage item will reappear. Beware that in the Third and Fourth Generations, there are moves that can steal or knock away your item.
For all battles, these rules should (and sometimes set by your console) be applied: 1) No Pokémon shall be over level 100. 2) No moves or combinations of moves can be on a Pokémon that isn't legal. 3) No items can be used. 4) No unofficial Pokémon. 5) No unofficial moves or items.