Aldonza's Top Ten Tips
Tip #1 ----------- Never, ever give a water-type Pokemon the Rain Dance move, which increases the strength of water moves.  Any electric Pokemon that's packing Thunder is free to wallop you across the arena.  The best Pokemon to use this trick are Raichu and Lanturn, who's part electric.
Tip #2 ---------- Always have a counter for the weaknesses in your group.  An example: Wildcat's Feraligatr, Pacman, is normally weak against electric-types and grass-types.  Thinking about this, he put in the Earthquake and Ice Beam moves, respectively.  This gives him a fighting chance.
Tip #3 --------- Beware the Pokemon that packs Metronome.  You'll never know what'll come out of it.  An example: Curtis's hometown "rival" has a Mew that knows Metronome.  Curtis's Tyranitar goes out to face Mew.  Mew uses Metronome.  Mew winds up with a one-hit KO move, Guillotine.  Tyranitar faints.  Curtis bashes his head against a wall repeatedly.
Tip #4 ------ The 3 M's of the Pokemon world ---- namely, Machamp, a Thick Club-packing Marowak, and Mewtwo ---- are possibly the deadliest Pokemon out there if they have the right attacks.  Have the appropiate counters on hand AT ALL TIMES if you don't have them already.  You'll be glad you did.
Tip #5 ----- Going along with Tip #2, never have more than one move corresponding to your Pokemon's type.  Try to vary your moves, and mix offense with defense if possible.  It'll be interesting to see what effective movesets you can come up with.
Tip #6 ----- Try not to have 2 Pokemon of the same type on your team.  Translated, don't have a Dugtrio and a Sandslash on the same side.  The "2-Pokemon-same-type" deal was the only way I could crush Wildcat's team, but there are better teams out there.  Also, don't attach attack-boosters, such as Charcoal, unless you need to.
Tip #7 ---- For you starters, raise all your guys equally.  You don't want to be stuck with 3 Level-50s and 3 Level-20s going into the Elite Four.  Taking advantage of weaknesses helps a lot.
Tip #8 ---- Unless you're giving them to Pokemon that know Mind Reader or Lock-On (or, in the case of Thunder, Rain Dance), avoid moves with lousy accuracy.  For instance, a Poliwrath that knows Mind Reader and Fissure can faint anything except fliers (and maybe even Mewtwo if 'Wrath has the Quick Claw).  Without Mind Reader?  He's hopeless.
Tip #9 ---- Try to wait to use TMs on your Pokemon until you've gotten as far as you can get in the game.  This way, you can make wiser moves when it comes to organizing your dream team.  I've made the mistake of not waiting at first, and I wound up with some pretty lousy teams when I first started out.  I eventually ditched the whole game and started over.
Tip #10 ---- Lastly, unless you have no choice, avoid the two-turn moves, such as Hyper Beam.  The damage done in the interlude can hurt you pretty badly.  The exception: use Sunny Day in conjunction with Solar Beam, and you'll be able to use it repeatedly until Sunny Day wears off.
Anyways, those are my tips.  If I think of anything else, I'll put it here.  In the meantime, go on!