It's migration season in Sinnoh, and wild pokes from across the land are all headed to Sinnoh. Your buddy, the Professor's assistant, has family in Sandgem town, and their little sister loves keeping track of what pokemon she's heard are landing in Sinnoh that day. Every day, you can talk to her and she'll tell you about what she's heard - both the specific Pokemon species that appears, and the area they'll show up in. You can then head to that area, and the Pokemon mentioned will start to appear in random encounters.
Keep in mind when chasing swarming Pokemon that they'll be of the same average level as other pokes in the general vicinity. If you hear there are Slakoth in Eterna Forest, expect them to be at around level 10-12. Most low-level pokemon won't be tough to catch even at full health, but the level 30 and above pokes might be a bit trickier. The levels of your main Pokemon team are likely in the mid-50s by this point, so if you're going for the catch, be careful not to overestimate your strength and KO the wild pokemon.
Swarms change daily, so keep checking back to learn what types of pokemon are available for the catching that day.
You might remember this place - it's located south of Hearthome City, and boasts a small garden where certain types of pokemon congregate. The fabulously wealthy jerkbag who runs this place is proud of the new pokemon that have recently been appearing in his garden (allegedly). Talk to him once a day and keep answering "yes" to his prompts to hear him babble about a pokemon that just showed up in the garden.
After he mentions the pokemon's name, you'll be able to encounter it in the garden. Keep in mind, however, that these pokemon are considerably rarer than the Roselias and Pichus that consistently infest the place. It may take considerably longer to run into the pokemon the old windbag spoke about than you would in a swarm situation.