Do you know how to use the rods in the first place? If you do, too bad!
First, use the rod in front of any water that requires Surf to get across. When using it, you may have to wait before a Pok?mon catches the bait. When you get a bite('Oh, a bite!), tap 'A'. Tap 'A' too soon and the Pok?mon will run away. Tap it too late and it'll run away too. The better the rod, the more likely you'll have to repeat those steps until you actually battle it. From there, the battles are all the same as on land.
If you battle a trainer with a Pok?mon that requires a rod, look it up in the Pok?dex and fish for them there. The only ones that you can catch by Surfing, rarely with rods, are Tentacool Tentacruel, and Marill. Also, you can only catch Relicanth, Clamperl, and Chinchou by Diving. Just about every other Water Pok?mon needs a rod to catch, besides Wingull and Peliper.