On the downside, too much paddle use too soon, or forcing your stroke into the wrong pull and recovery pattern, can lead to swimmers' shoulder problems. The best way to avoid that is to build up slowly, over multiple weeks, adding a little bit more time pulling each workout until you reach your goal distance.
How far should you pull in a workout? That is up to you. I think anywhere from 10% to 50% is OK, depending upon your aim or your goal for that swim workout, the type of swim paddle, and depending upon what you do with the paddles.
Using them as a tool to build proper stroke technique could mean using them often but not continuously. You might wear them for a few laps, take them off for a few laps, then repeat.
If the goal is to build swimming strength (strength-endurance in the water, as opposed to general dryland strength training or swim-specific dryland strength training), then wearing paddles for longer durations may be in order. Wear them as part of your warm-up, possibly even 33% of the warm-up, then take them off for the rest of the workout. Alternately, put them on for part of, or all of, a main set. I do not suggest trying to sprint with paddles unless you have used them for a long time and do not have any shoulder problems. Even then, do so with caution. That does not mean you should not try to swim at a fast pace with paddles on, you can and should sometimes, but swimming a maximum short duration effort with paddles on can cause serious damage before you realize it.
I like paddles to be used for some easy swimming to remind a swimmer of good stroke patterns, and for some faster pace swimming to put some extra load onto the swimmer during a workout. I most often recommend that paddles are used along with a pull buoy to emphasize the load on the upper body.
Let's take a look at some of the paddles from Finis. They offer a variety of interesting paddles. Theirs are not necessarily better for you than another brand of swim paddle, but I do think highly of the company and the products they sell. I have purchased my own set of all of the below except for the PT Paddle. Those I have borrowed from other swimmers form time to time. There are plenty of other paddles on the market that have their place in the swimming pool, too, like the Han's Paddles, Techpaddle (a 10/10 for technique), the Star Swim Paddles, FAST Paddles (a 10/10 for strength), and many other paddles.
Strength Use 4/10
Forearm Fulcrum Paddles: I use these paddles every time I swim, during my warm-up. I do not like them, but I know they are good for my stroke, so I use them! They make me remember to swim with a high-elbow freestyle, using my own strength and movements, guided by the pressure the paddles put on my hand, wrist, and arm. They are very much a technique paddle, but because my hand still catches water, and my pull is in the right orientation, I am getting some strength benefits, too.
Strength Use 7/10
Agility Paddle: These paddles are strapless - pretty cool - and force swimmers to pay attention to what their hands are doing on both the recovery and the stroke. A bad entry or siding the hand outward too much during the pull and the paddle lifts away from the palm. Instant feedback. I have tried these paddles for several weeks (my wife has them most of the time) and think they give good technique feedback. They are also useful for strength building.
Strength Use 6/10
Freestyler Paddles: These may be my favorite paddle. I am an advocate of finger only paddle straps (Agility Paddle aside), where the only thing holding the paddle in place is an elastic cord that loops around the middle finger. You can cheat and use your thumb and pinky to hold the paddle, but hey, that is cheating! With a finger-only paddle retention system, if you pull in non-linear path from front to back, if you do a lot of hand sliding side to side, the paddle moves on your palm. It twists out of its proper orientation. Instant feedback again, telling you that you are not taking the best pull path to maximize forward movement. The Freestyler paddle adds a "keel" along the lower surface, meaning that almost any sideways motion results in the paddle shifting. It teaches a great, linear pull pattern for freestyle. Hence its name, Freestyler. It is not as good as some larger surface paddles are for strength building, but it can be used for that, too.
Strength Use 3/10
PT Paddles: I have only used these paddles a few times. They are not aimed at strength building, although you will develop that, in the proper path, if you use the paddles enough. The PT Paddle's focus is on making you catch the water and pull with proper arm orientation. It is a half-dome shape, with the flat part nestling on your palm and fingers, the curved part out. If you try to pull with just your hand, you get nothing. You have to get into a high-elbow catch position and press on the water with your wrist and forearm. Do that right, often enough, and it becomes automatic. Automatic what? Automatic good catch position, good stroke technique, and good swimming.