This is the standard view for me when riding with the full-time cyclists.
You are a triathlete. That means you train for three sports simultaneously. You are (as one of my friends once put it) striving to be solidly mediocre in three sports. That means that when you pit yourself up against dedicated swimmers, focused cyclists, and well-trained runners, you are probably going to come up short. Why? Because you're not trying to be the best swimmer, biker, or runner; you're trying to be the best triathlete.
But when the triathlon season is over, there's no reason to continue to pursue adequate mediocrity in three sports at once. Why not focus on just one sport, and get really, really good at it? What if you can make your "solidly mediocre" as good as a single-sport athletes' top performance?
It was this step, more than any other, that brought me more success as a multisport athlete. Running was always my weakness. I didn't like it; I didn't want to do it; it was my primary limiter in every race I did.
But I signed up for a half marathon anyway. And then I did another one. And somewhere in that training to go long, I encountered a runner within myself that I didn't know existed. I started to enjoy running, to look forward to it, to consider myself a runner. Of course, once the triathlon season came back around, I became (once again) a triathlete. But the hard work I'd put in and the improvement I'd seen stuck around, and by this season, I was running 8:30/mile instead of 9:20.
My guess is that for most triathletes who weren't previously athletic, running is the limiter. If you came from a running or cycling background, swimming is probably your biggest struggle. If cycling is your weakness, that's completely legitimate, too. Whatever your weakest sport is, you need to figure that out (I bet you already know it, if you think about it). My recommendation to you is that you do an end-of-season focus on that sport.
The alternative to choosing your weakness is to choose what you like. You probably won't see as much benefit going into next season, as far as catching up to your competition, but you will still come back stronger, more capable, and more confident in your abilities. Last year, I focused on a half marathon at the end of the season, and it saw my average speed drop by 50-60 seconds per mile; this season, I'm focusing on cyclocross and group riding, and I think by the end of next season, I can easily be averaging 22 MPH. That's not going to provide as great an edge as if I were to drop my run times by another 30 seconds per mile. But cyclocross is fun and I'm enjoying racing with my cycling team. (FYI, I'm planning to do a half marathon and marathon after the cyclocross season).
Once you figure out which sport you're going to focus on, here's what you do:
Swim: Find a swim meet in your area or close enough to drive to. Determine which events you'll compete in. Challenge yourself! Don't do three long-distance freestyle events; try the 100 breaststroke, or the 200 IM. Developing your skills in the other competitive swim strokes will give you more overall strength and confidence in the coming year, as well as balance out your muscular engagement (which will reduce your chance of shoulder injury).
From there, you have two options: join a masters swim team and work with them on preparing to race your target meet, or prepare on your own. If you're going to prepare on your own, you need to make a plan. It could be as simple as committing to swim 5 days a week; it could be as involved as building a periodized schedule with weekly yardage and daily training objectives. Read up on swimming--coaching techniques, tapering, stroke mechanics, and so on. The more you learn about your swim stroke from this phase, the more you'll have to bring into your next tri season. If you're going with a masters group, be sure your coach knows about your plans and goals; he or she might not write up a whole plan for you, but you'll get some more specific help in workouts, and maybe even some workouts written with you especially in mind.
Bike: Again, you pick an event. It might be a race. It might be a series of races. It might be a tour; check at a local bike shop, as they'll usually have flyers up, or will at least know the cycling scuttlebutt. Whatever your event, commit to it (psst: that means go ahead and register!). Once you've chosen what to do, start riding with a group. Start with a casual, local ride; again, check with a local bike shop. Be sure to ascertain what kind of pace the group keeps (you need to be able to hang in) and what kind of purposes the ride serves. If you're racing (as opposed to doing a long tour), I highly recommend you find a friend who's into the cycling scene and has some experience with racing. Cycling races aren't quite as beginner-friendly (and not nearly as welcoming) as triathlons. Be prepared for that.
Commit yourself to getting out of your comfort zone. If you're used to riding triathlon-style, you probably prefer to train by yourself. You're not necessarily used to hanging in a draft; you don't often need to feel responsible for holding your line. These are things that are valuable for a triathlete to learn and be comfortable with, just likes it's beneficial to be able to swim all four competitive strokes (yes, even butterfly).
Run: This is probably the easiest of the three to focus on in the off-season. You have a few options available to you as far as how you pursue this emphasis, but all of them start with the same basic premise: choose an event! Maybe you want to gun for a PR at the mile, 5k, or 10k distances. Maybe you want to run your first marathon or half marathon. Maybe you want to try something new, like trail running. Whichever it is, choose an event and commit to it (yep, that means register)!
If you're prepping for a PR, you should already have run the distance you'll be gunning for. You should have an appropriate base of distance built up. And you should already have been working in some intensity (i.e. sprints, intervals, track work). Set up a detailed plan with a couple of speed workouts a week, a long run that isn't more than 50% of your weekly volume, and some cross-training. If you're looking for speed, I recommend 5 days of running per week; if you're not running at least 4, are you really doing a single-sport focus?
If you're shooting for your first half marathon or marathon, it's all about building distance slowly and safely. Otherwise you get hurt. Plan on 3-5 days of running per week, with at least 2 days of cross-training. Look not so much at daily volume as weekly volume, especially at the beginning. The long run becomes all-important eventually, but at first you need to accustom your body to taking so many miles. When in doubt, take it slow. Never increase weekly mileage by more than 10%; never increase your longest run by more than 10%. And don't do all your mileage in one big, long run!
The main physiological benefit you derive from a single-sport focus (in my opinion) is putting in all the time. Because you're not dividing yourself (at least) three ways (we're not even getting into weight lifting, flexibility, yoga, and bricks), you have a lot more time and energy to devote to quality workouts in a single sport. And that leads to big improvement fast.
But equally important is the psychological benefit--you become more confident. I went last year from claiming that my strength was transitions to firmly believing "I am a runner!" And the same will happen to you, whether you choose to spend this season focusing on swimming, biking, or running (or something else entirely; why not focus on weight lifting or yoga?).
So. Which one will you be doing?