You bet and is it fun! First, you need a boat stable enough to pass the snack test(are you comfortable sitting in the boat, not holding onto the paddle?). For those who like to use rods, we recommend the "Fish-On" rod holder for trolling. People who are fishers first and paddlers second like to mount it forward of the cockpit. For the paddler who likes to fish, mount it aft of the cockpit. We like to use a "mooching" rod because is long enough to play the line all the way around the ends of the boat when you have a fish on that likes to run.Hand lines can be made out of anything you can wrap fishing line around and are great for jigging for bottom fish. People in our area, the northwest, tell exciting tales about tying into king salmon. In Texas we hear that kayaks are great for getting into the shallows of the Gulf for redfish. Paddlers in southern California hang near the kelp beds and haul in calico bass all day long. It's easy and simple, just like kayaking (most of the time).
Suggestion: Do not use a stringer in salt water, predators like large ling cod or sharks may be attracted to your catch. For larger fish like Salmon or Ling Cod, try using a hand gaff through the gills to hold them while you dispatch them, then use a heavy plastic bag inside the cockpit for storage until you get back to the beach. It helps keep "that fishy smell" out of your boat, and fin quills out of your legs.