As you enter the Gym, you'll be given some Fresh Water by Clyde. Cool! Anyway, Roxie's Gym is pretty straightforward — it's basically a rock club and they're rockin' out to the theme of P-O-K-E-M-ON. You just need to take on the band members before taking on Roxie herself, so go ahead and start with them.
The drummer (a Roughneck) has a Grimer L14 and a Koffing L14. The Guitarist has a Venipede L14 and a Koffing L14. They shouldn't be too tough to take down unless you started with Snivy; if you did, hopefully you caught some other Pokemon to help fight them, because it may be a little rough with just Snivy. Magnemite is an awesome Pokemon to use here, since it can't get poisoned and isn't affected by Poison-type attacks.
Before taking on Roxie, I recommend you give your Pokemon (other than Magnemite or Venipede) the Pecha Berries that Cheren gave you earlier. These will heal poison instantly, and that's a huge part of Roxie's strategy, so beating her to it is important. Whenever you're ready, talk to her and take on the second Gym Leader of the game!
Roxie's Koffing has quite high Defense, making it tough to take down. Special-based attacks are the way to go against it. If worse comes to worse, though, you may be able to take it out with your Snivy or preferably Servine, assuming you are at least level 16 and can use Leaf Tornado to lower its accuracy (being at least a Servine is highly recommended, though). Make sure you have a Pecha Berry equipped if you do that, though.
Her Whirlipede is really the thing to worry about, though, as it has Poison Point, which will poison your Pokemon that make contact with it. That invites it to use Venoshock, which gets double power if the foe is poisoned, resulting in catastrophic damage! It's important to avoid being poisoned at all costs.
Fighting Roxie with Metal!
If you're really struggling against her, just go catch a Magnemite in the Virbank Complex, train it up to level 11 so it learns SonicBoom, and then just keep using that against her two Pokemon. Don't forget to laugh. It's extremely easy if you do it this way.
After beating her, she'll give you the Toxic Badge, which ensures all traded Pokemon up to level 30 obey you without question. She'll also give you TM09 (Venoshock), a 65-power Special-based Poison-type attack that doubles in power if the foe is poisoned. It's great on Koffing, but it's also not too shabby on Venipede, too, thanks to its Poison Point ability.
Just as soon as you get off the stage, someone from the audience will come up to you and say that they were very impressed with your work and you should consider acting at the Pokestar Studios. Well, naturally that upsets Roxie, so she heads off. You should do the same! You've definitely gotta go check out Pokestar Studios, which can be found north of Virbank City, because now may be your chance to hit it big.