Have a read of this
http://forum.realsurf.com/forum/viewtopic.php?t=12430 (if I can direct people to another forum!) which talks a lot about paddling and technique and a few other associated things.
There is nothing that will improve your paddling as much as paddling. Swimming is obviously the closest activity and should be your main activity (I have seen people say 'put your board in a lake or dam or river and just paddle', which is a great idea if feasible).
There is no way to build up shoulder muscles other than through resistance exercises (ie lift weights). That said, its not just your shoulder muscles, its your back muscles as well, so don't forget them.
If you google around there are about eleventy billion exercise programs. I am a bit of a gym bunny (um, the male version - gym hare?) myself and could probably give you 50 shoulder and back exercises off the top of my head. However, if you are beginner to weights, read up on and watch training videos for: pull ups/chin ups, shoulder press, bench press and rows (which are, respectively, vertical pulling, vertical pushing, horizontal pushing and horizontal pulling). Those four exercises will cover you for your first 3-5 months (and there are plenty of variations just within those).
However, dont be a 'popsicle' - all upper body and no lower body. Do some squats (look up goblet squat to start), leg presses, unilateral leg exercises - split squats and the unilateral RDL, which is excellent for balance as well. Core exercises (not sit ups - bad! Look for Pallof presses and anti rotation activities). If you don’t have access to a gym, look for body weight versions of these exercises (eg bench press = push up), although you can be a bit limited for some things.
That said - I have done strength training at least 2 or 3 times a week for the last 15 years and I don’t live near the beach; and think swimming is very boring and hate doing it, but I ride a bike for 1/2 hour every day for cardio and, well, I totally suck at paddling. I assume I am better than I would be without the gym and cardio, but the gym and cardio don’t cure the problem.
Paddle and swim. Resistance exercise is good for your health, so do that as well.