Here's one way to structure a strength training program for the off-season. This all assumes that you are currently in the prep/base phase of training and you have several months before you begin racing. The goal is to get stronger while your swim/bike/run training schedule is relatively light and you can afford to hit the weights hard a couple times each week. Once you get into your build phase and racing season, you won't be able to get any hard lifting sessions so you'll be focused on maintaining strength with a quick circuit every 7-10 days.Exercise types
Stick with compound movements that work multiple muscle groups and simulate the type of mechanics our bodies are designed to do-consider these "structural" exercises. Isolation exercises like bicep curls and leg extensions might be useful for bodybuilders who lift for appearance but don't compare to "structural" exercises that use lots of muscles in a coordinated action for building functional strength that can be directly applied to our sport.Avoid the machines as much as possible; chest/shoulder (pressing) machines should be avoided at all costs. Most "pulling" machines are actually okay. Most "pressing" machines don't allow your joints to choose their own range/path of motion and force both shoulder joints to have the exact same movement path. Some people will suggest machines for inexperienced lifters to avoid injury, but in reality, free weights are only dangerous if you are trying to lift too much weight. So start very light and you'll be fine.Recovery
Allow plenty of time for recovery between lifting sessions. Depending on whether you decide to do total-body workouts or "split" workouts, 2-3 sessions of 30-45min per week is plenty to build strength. To be effective, muscle-building, exercises must inflict some damage to your muscles. The key is to then stay away from the weights long enough to let your body repair that damage. The results are bigger, stronger muscles. Try to hit everything once per week with the exception of abs/core which you can work 2-3 times per week.Progressing
Try to make progress every single session. This might be a higher volume of repetitions (add one rep to each set or even one rep total), heavier weights (same sets/reps but with 5lbs more weight), or (more likely) some combination of the two for each exercise. For example, I do pull-ups a couple times a week as part of my strength training. I started with 3 sets of 6 reps (6,6,6) and have been adding a single rep each session for the past few weeks (7,6,6; 7,7,6; 7,7,7; 8,7,7...) last week I was up to 10,10,9 but I decided to change things up a little the other day and did 5 sets of 6 reps (6,6,6,6,6) instead. I still only added one rep to my total but changed the stimulus my muscles got and I can honestly say I felt sore from pull-ups for the first time in a couple weeks.A typical routine
With those basics in mind we can build a very simple strength training routine that you could do 2x per week and get a great total-body workout. Squats, deadlifts, lunges, bench press, pulls-ups, and shoulder press. Ideally, split these up into 2 sessions (back/chest and legs/shoulders). Other variations may be better for your schedule.
Squats, deadlifts, and lunges are great for your legs, back, and core. They are typically done with a barbell but if you don't have experience with free weights then go ahead and start without any weight or just use a light bar without any additional weight for a couple of sessions to get the feel of the technique.
Bench press works the chest, front shoulders, and triceps. Pull-ups work the back and biceps. Shoulder presses primarily work the shoulders. If you can't do more than 2-3 pull-ups then use the lat-pull-down machine instead. Keep the weight light enough so that you can pull it down to your chest with a slow, controlled motion and don't feel the need to throw your weight into it. The bench, shoulder press, and pull-ups are basic push and press movements but there are many variations that can be done in a gym or at home with some dumbbells and a stability ball, including chest press (flat, incline, decline : barbell and dumbell), dips, and rows (bent, seated, and upright-barbell, dumbell and cable), and shoulder presses (barbell and dumbell). Switch between barbell and dumbbell for the presses from week to week. They provide a different range of motion and change the stimulus slightly.Periodizing your plan
A classic 3 phase periodization plan would go something like this:
Anatomical adaptation (2-4 weeks)Start with 3 sets of 15-20 reps of each movement 2x per week for the first 2-4 weeks. This is called anatomical adaptation and it basically conditions your muscles to start lifting heavier weights and build strength and power later. Remember, the goal is to make incremental progress every session so try to add either a rep or some weight each time.
Hypertrophy (4-6 weeks)Once you get comfortable with the exercises and your muscles get "broken in," you'll want to start increasing the weight and decreasing the number of reps. Generally speaking, heavy weight and low reps increase strength most effectively. Here you'll increase the weights and decrease the reps per set to 8-12. Try to pick one exercise to focus on each session (bench press for example) and do 4X10 and then 2 sets of 10-12 for another 2 exercises like dips and dumbell (DB) incline presses. Add 4X10 deadlifts, 2X12 pull-ups, and 2X12 rows and you've got a great upper body session. Stay in the hypertrophy phase for 4-6 weeks and continue to strive for incremental progress every session. This shouldn't bulk you up significantly since you'll only spend 4-6 weeks in the hypertrohy phase and then move to strength/power.
Strength/Power (4-6 weeks)Finally you'll move to the strength/power phase. Weights will increase again and reps will decrease to 5-8 per set and you might be doing 4-5 sets per exercise. Here we're no longer focused on bigger muscles but improving power by starting to lift with more explosive movements. This is where that strength you gained in the last phase gets transitioned into something useful. Again, go 4-6 weeks with this phase if time allows.
Maintenance (higher-volume triathlon training and racing)Once you've gone through this basic periodization progression you should be getting into the higher volume part of your triathlon training and you might even be picking up some more intense bike and run sessions. From here on out you'll want to move to a maintenance phase for the rest of the season where you move back to moderate weights and lift 2-3 sets of 12-15 reps once or twice a week as your training schedule allows. I personally back way off the weight room from mid summer on out because I just don't need any additional work for my legs and I can't afford to use my lighter days for something strenuous like lifting.