When I was younger I would just use Groudon, Kyogre, Rayquaza, Giratina, Infernape and my Level 100 Blaziken, hoping for a super effective or OHKO hit. Now I'm 13, I use different styles.
My Snorlax in HGSS single handedly took down a Regice, Regirock and Registeel, all at my level by using rest and Giga Impact. I like using raw power, with Pokemon like Blaziken, Aggron and Lucario.
Another thing is being a nuisance(A la Emolga and Raichu). Raichu and Emolga both know Double Team and Thunder Wave, with the latter being taught Swagger as well. When I replayed Emerald, I made sure my Lairon used Iron Defence all the time. It took pathetic damage from even the most super effective moves.
I also make sure my Pokemon have STAB moves and at least some type coverage(My Salamence knows Flamethrower, my Blaziken knows Earthquake, my Lucario knows Crunch...)
In general, I'm an offensive player, with quite a few aces up my sleeve.