We've discussed the basics of battles and a lot of nitty-gritty details too, but to truly understand Pokémon battles you need to get out there and experience all kinds of exciting battles! Until you get to that stage or if you just need a gentle reminder, here are some important tips from the Pokémon veterans over here.
Same-Type Attack Bonus
When traversing the wilderness of the Internet or hanging around with hardcore Pokémon fans, you may hear comments like "Milotic's Surf has STAB" and then ponder to yourself "whatever does that mean?"
STAB stands for Same-Type Attack Bonus and what it means is that Pokémon using moves the same type as themselves will do 1.5 times more damage than usual. In Milotic's case, it's a Water-Type Pokémon and Surf is a Water-type move, so Surf will do 1.5 times damage in Milotic's hands (or whatever it has for hands).
The point of STAB is to encourage and reward Pokémon for using moves of its type. For instance, a lot of Water-type Pokémon can learn Ice-type moves, so what's the point in using Ice-type Pokémon? Well, Ice-type Pokémon will do extra damage with those same Ice-type moves.
If a Pokémon is dual-typed, it will have STAB with both types of moves, making it a very versatile Pokémon. As a general rule of thumb, having moves with STAB is preferable. However, it's also recommended to have moves without STAB for reasons we'll explain next...
Variation Is Good
At some point you must have thought to yourself "Hmm, these Gym Leaders sure are easy, since they all use one type of Pokémon".
The same principle also applies to yourself: always avoid putting yourself at a disadvantage by not having a varied team of Pokémon. If you have an all Fire-type team, you're going to struggle against Water, Rock or Fire-type Pokémon, for example.
Since you can field six Pokémon and Pokémon can have two types at most, you can represent 12 of the 18 Pokémon types with Pokémon alone. For the missing types, you can give your Pokémon moves from that type, via TMs or other means.
Although this means not getting STAB, if you encounter a Pokémon weak to or double-weak to that type, you can still do double or quadruple damage. For the main quest, you don't actually need to cover all your bases, but the more variety the better!
Introduced in Pokémon Diamond and Pearl, as well as being aligned to 1 of 18 types, all attack moves are either Physical-based or Special-based . The move's designation affects which of your Pokémon's stat it runs off and which of the opposing Pokémon's stats it targets.
Physical-based moves are powered by your Pokémon's Attack and reduced by your opponent's Defence . Similarly, Special-based moves are powered by your Pokémon Special Attack and reduced by your opponent's Special Defence .
On your side, if your Pokémon has much better Attack than Special Attack, you should focus on using Physical-based moves. However if the opponent is a massive Defence tank, you may want to switch to Special-based moves.
The EV Difference
STAB and the Physical/Special Split may not be obvious at first, but EVs are completely hidden from your eyes... sort of. EV stands for Effort Value ; your Pokémon gain EVs for each of the six stats (HP to Speed) when they defeat other Pokémon - the type of EV depending on the Pokémon species.
We won't go into detail here (see Super Training in the Extra Modes chapter for the full scoop), but EVs basically slowly improve your Pokémon's stats - this is why Pokémon trained over a long time are better than wild Pokémon of the same Level.
In the main quest, sticking with Pokémon found early-ish is generally a good idea, as they've had more time to gain EVs and thus typically have superior stats. But if you're smart with your strategy, even later Pokémon you catch (with no or less EVs) can still hold their ground. If you do need to boost your EVs fast, you can use the new Super Training mode.