Since the Eterna Gym is a Grass-type Gym, you'll want to stock up on status-healing items before you even walk in the door. If you remember Erika from Red/Blue/Yellow (or FireRed/LeafGreen), you know what I'm talking about. Your Fire- and Flying-types will serve you well here. If you started with Chimchar, you're lucky, but those Trainers who started with Turtwig or Piplup can still win with a Staravia. Failing that, it's possible to catch Ponyta in the grass just east of Eterna City, but I highly recommend that you train it first.

The Eterna Gym is located near the southern exit of the city-it's pretty hard to miss. Although the Gym's structure seems simple enough, you can't battle Gardenia right away-first, you must find her Junior Trainers who are hiding in the Gym. I'd tell you where they are, but the Gym puzzles to come are far more difficult, so a little practice doesn't hurt. Gardenia will battle you with these Pokémon:

Lv. 19 Cherubi Type: Grass Weaknesses: Bug, Fire, Flying, Ice, Poison

Lv. 19 Turtwig Type: Grass Weaknesses: Bug, Fire, Flying, Ice, Poison

Lv. 22 Roserade Type: Grass/Poison Weaknesses: Fire, Flying, Ice, Psychic

Leech Seed can be avoided by switching your Pokémon out, but you lose a turn to attack. (Also, Grass-types are immune to Leech Seed, but I wouldn't recommend using a Grass-type Pokémon in this battle.)

If you win, you get the Forest Badge, which allows you to use Cut outside of battle (you can get Cut from Cynthia north of the Gym before you even come here) and makes traded Pokémon up to Lv. 30 obey you, and TM86 Grass Knot, a Grass-type variation on Low Kick that does more damage to a heavier opponent.

There is an item amongst the trees behind the Gym. Maybe it's a gift from Gardenia :-)

"What's that I hear you saying? You think you have me cornered?" -Gardenia