Wild Battle Example:
"Chik, chiko…" Chikorita growled. The three stood in silence, staring ahead of them, waiting. Suddenly, a cry came from above and as Shadow aimed the light upwards, a small flying figure dove downwards.
"Ri!" Chikorita cried. Shadow aimed the flashlight back in her direction. A small, blue bird had perched on top of Chikorita's leaf and was pecking at it vigorously.
"It's… a Taillow," Shadow sighed. "Throw it off, Chikorita!"
Chikorita, previously curled up into a ball in a futile attempt to protect herself, stood up and violently whipped her leaf forward. The Taillow was hurled a short distance away, but managed to right itself in midair. It chirped angrily at Chikorita before diving again.
"If it's a fight it wants…" Shadow said. "Vine whip, Chikorita! Knock it out of the air."
"Rita!" Chikorita extended two vines from the rings around her neck, a skill she and Shadow had practiced for hours back during his work at the lab, and launched them at the incoming Taillow. The tiny bird only barely slipped around the first vine, but was swatted away by the second and thrown harshly into a tree trunk off to the left of the path.
"Again," Shadow ordered, as the tiny bird bravely took flight again, despite its injuries. Chikorita obeyed again, hurling her vines at the bird. This time, however, the Taillow took a dive underneath the incoming attack, leaving the vines to whip the tree. In one fluid motion, the Taillow spread it's wings and pulled up faster than Shadow's flashlight could follow, gliding along the dirt and speeding into Chikorita with a Quick Attack. She was thrown off her feet, but managed to stand and growl at the tiny bird, who had once again taken to the sky and was coming around for a second attack.
"Stubborn little bird," Shadow said. "Tackle attack!"
Chikorita immediately charged right into the path of the oncoming Taillow. With a cry, it picked up speed, going for another Quick Attack. Chikorita lunged forwards as Taillow approached and the two collided. Both Pokémon hit the ground hard, but both stubbornly struggled to their feet again, refusing to give up.
"Hold up, Chikorita," Shadow said, whipping his backpack around and pulling out a pokéball. Chikorita looked back in confusion, wondering why she was told to stop attacking the intruder. Shadow, meanwhile, tossed the pokéball at the Taillow, and just clipping a wing as the bird tried to avoid it. The pokéball opened as Taillow was dematerialized into a red light, and then sucked inside. The pokéball then sealed and fell to the ground, where it proceeded to shake as the Taillow resisted.
Okay, so. The main difference between a wild battle and a trainer battle is that for wild battles, no one tells the other Pokémon what to do. Without another person to command the opposing Pokémon, basically it helps to somehow write in what attack it's using so the reader doesn't go "well what the hell did it just do?" Also, notice that although type differences still exist, some attacks might still be effective, whereas in the games it wouldn't make sense to use, such as using Vine Whip to throw Taillow into the tree, despite the fact that Grass-Type attacks normally aren't very effective against Flying-Types.
Trainer Battle Example:
"Let's start this off with, uh…" Carrie had to stop and think. Zubat wouldn't be easy to tackle while in the air. That left Ember as her only offensive option. What else could Cyndaquil do? "Use Ember!"
"Counter with a Gust attack!" the boy shouted. Cyndaquil lit the fire on his back before launching a barrage of tiny fireballs at the flying bat, while the furious beating of the Zubat's wings generated a blast of wind. The swirling miniature tornado easily dispersed the tiny flames, as well as pushing Cyndaquil backwards.
"Hold on," Carrie said irritably, taking out her pokédex and pointing it at Zubat. The pokédex didn't seem to respond, but when Carrie looked at the screen, a blob of text had appeared and she remembered that she had turned the audio off. Passing over Zubat's data, she checked their list of moves instead to get an idea of this Zubat's level. She noted, however, that Gust was not on Zubat's list of natural abilities. Further down the list, she found that Zubat could learn a variety of attacks in addition to their natural ones, including Gust, with a bit of focused training. Curious, she pointed her pokédex at Cyndaquil next, who had turned his head to see why his trainer stopped calling orders.
"Zubat, use Supersonic!" the boy shouted, tapping his foot impatiently. His Pokémon responded obediently, opening his mouth and letting out an odd sound wave.
"Hey!" Carrie whined as Cyndaquil crouched to the ground in pain from a sound that was too high for Carrie's ears to hear.
"You can't just pause a battle," the boy responded. Carrie hissed in annoyance and quickly scanned Cyndaquil's current abilities as the boy continued. "Do a Leech Life attack!"
"Smokescreen!" Carrie ordered, after seeing the move on Cyndaquil's list. Her Pokémon, still covering his nonexistent ears, began letting off a large cloud of smoke from his back, much like he had done back in Elm's lab. The Zubat, who had flown in for his close-range attack, quickly pulled up, avoiding the cloud that had hidden his opponent.
"Now, Tackle it!" Before the boy could reply, Cyndaquil had leapt from the smoke and rammed his body into the bat, throwing him back, but he regaining his flight easily. "Now get back in the smoke," Carrie ordered, and her Pokémon obeyed.
"Have it your way," the boy responded. "We could just blow that away, but why don't we show off a bit? Zubat, find Cyndaquil and aim an Air Cutter at it. And keep your distance!"
Carrie flipped back to Zubat's list. Air Cutter was another move that Zubat couldn't learn without proper training; the boy was better than his appearance let on.
"Um, try another Ember," Carrie suggested, unable to think of anything else to do. Cyndaquil agreed, and another small barrage of fireballs erupted from the smoke. Unable to aim, Cyndaquil's attack didn't even come close to the Zubat, who meanwhile was using his natural ability to see with ultrasonic waves to find the fire Pokémon. As the Zubat received confirmation of Cyndaquil's location, he flapped his little wings in specific patterns, causing tiny blades of air to shoot into the smoke. Cyndaquil screamed from somewhere inside the cloud even as the wind blew it away. When it had all but dissolved, Cyndaquil was laying on the ground, unmoving.
So here's a trainer battle. Much easier to write, I think, since both sides are flat out saying commands, no having to work in the name of the attack anywhere. Only thing to point out here is to remember that real-time battling isn't much like the games, where it's back and forth, and moves only affect the opponent… they can in reality affect the area and even the Pokémon that used the move, as shown here… Cyndaquil used Smokescreen to hide itself, but later on, that same smoke cloud prevented him from aiming his own attack because he couldn't see the target. Also, common sense (which I pointed out but, due to the trainer's confidence/showing off, he didn't act upon) : Smokescreen is easily blown away with wind. This makes things like Double Team much easier to handle in reality than in-game, because the copies, once you know they're fake or if you manage to land a hit on the real pokemon, disappear (according to the anime), or at the very least, your character will know not to target that copy again.
Double Battle Example:
(For the sake of avoiding all confusion, it's Carrie/Spinarak + Kit/Fearow vs Tori/Staryu + Nichole/Hoppip)
The referee waved a green flag, and Kit's Fearow immediately dove for Nichole's Hoppip without a command. The Hoppip shrieked, ignoring Nichole's tackle command to cover her eyes with the leaves on her head instead. Tori ordered Staryu to step in and slow Fearow with a Water Gun attack. Her Pokémon obeyed, but the stream of water was much too weak for Kit's higher leveled bird to be hindered too badly. The Fearow's large beak jabbed at the cowering Hoppip, catching one of her leaves and carrying her into the air.
"Spinarak, use String Shot!" Carrie ordered. Spinarak looked back at her for a moment, then shot a thin string at Fearow, which tangled in the bird's wings, slowing his flight.
"What the hell are you doing? Seriously!" Kit shouted at Carrie. She then turned to her Fearow and ordered, "Do a Faint Attack!"
Fearow suddenly took on a black aura for a fraction of a second before disappearing completely, both the string and Hoppip falling to the earth. Before either one landed, though, Fearow reappeared in another black aura and rammed hard into the Hoppip.
"Star, try another Water Gun!" Tori shouted. Again, Staryu launched another stream of water at Fearow, but this time the bird dodged it completely, flew in a circle, and dove at Staryu, striking it with a wing before pulling up again.
"Peck the Staryu, now!" Kit ordered.
"Star, wait until it hits you, then Recover!"
"Spinarak, don't let Staryu heal itself!" Carrie cried, whipping out her pokédex. As Fearow dived, she said, "Can you do a Constrict attack?"
Spinarak responded by charging at Staryu. Fearow struck Staryu's core with his beak before flying up again. While it staggered, Spinarak clung to the star, gripping it with all of his legs, and tightly wrapping a string around it.
"Try to tackle the Fearow again," Nichole ordered. Her tiny Hoppip regained her balance and flung herself towards Fearow. The bird simply beat Hoppip with a wing, flinging it back to crash into Spinarak and Staryu.
"Finish them," was Kit's only order. Fearow dove down a third time, both wings spread wide, and slashed at all three other Pokémon. They all were thrown hard into the ground. Fearow returned to the air, but none of the other three made any move. The referee waved his red flag over the three of them and declared them all knocked out.
And here's the double battle. Again not the best example, but it might help when you're dealing with large amounts of trainers in a fight at once. Also notice that Fearow acts without an order several times. Don't forget that Pokémon have minds of their own as well as their own survival instincts and will probably take actions once in a while to attack of defend without being told to, which Nichole's Hoppip shows when it ignores her order in favor of trying to defend itself.. After all, if someone was shooting fire at you, would you need to be told to get out of it's way?