From my experience, there are three main ways to play offense: Boom offense, Paraspam, and Spike abusing. (BP counts too I guess, but in my mind BP is a seperate playstyle on its own along with Offense, Balance, Defense, and Stall, so it's not included here.)
Paraspam is just that - instead of exploding on potential targets, you aim to paralyze them. Several offensive mons heavily appreciate Paraspam, such as Marowak, Curse Heracross, Tentacruel, and pretty much any Belly Drum user. The benefit to this over Boom offense is that it's a much safer option, and you obviously have the Pokemon afterwards after you para'd something.
Spike abusing is when you take Pokemon like Nidoking, who are a pain to deal with offensively but just barely miss out on a lot of 2HKOs, and put a greater emphasis than normal on setting up spikes for them to abuse. Here, the spikes are used less as a source of chip damage, but more as a way to pseudo-buff an attack's power when hitting a Pokemon on the switch. Common Pokemon are Zapdos (as opposed to Raikou), Nidoking, Machamp, Tyranitar, and Gengar as spike abusers. Gengar can also boombait if your team appreciates it.
Of course, it's possible to combine all three; boom-baiting + paralysis + spikes isn't entirely out of the realm of possibility.