I'm obviously not one of the really muscular guys on this site, but I did just start working out between 1.5 and 2 years ago, so I have some memory of what this is like. I could go into more detail about what I've done, but I think it's better to answer you in more general terms.
This is vague, so forgive me, but the most relevant point I can make is you'll probably see the best results by starting out small and making constant small-gain goals for yourself. Long term, you're better off viewing exercise and dietary changes as long-term investments rather than aiming for specific events like a class reunion or a day to hit the beach or whatever. A lot of resolutions to lose weight and exercise more and get in shape fail for a combination of two reasons: people try to do too much too fast and the first time they miss a goal they feel like they've failed and give up; or people make the goal too undefined. So don't try to just mimic what the guys you want to look like are doing, and don't be discouraged if you have to start out with very light weights or can only do one set of something. In the short term, your goals should be more along the lines of "This week I did 8 reps at 10 pounds. Next week I'd like to do 10 reps at 10 pounds. The week after, I'd like to do 6 reps at 15 pounds". than "I want to bench press my weight". That can be a good long term goal to stretch for, but if you're just starting out, don't expect it to happen soon. Health as a goal is better treated as a marathon than a sprint.
If the reason you're only going to be at the gym twice a week is financial rather than due to your willingness/ability to exercise more frequently, I'd focus at the gym on things which are much harder to do without gym equipment--you can in theory walk or jog in your neighbor, take the stairs instead of the elevator at work, etc without a large investment, while at the gym you'll have the advantage of weights and machines that are a lot more effort to have access to outside of the gym. You can apply the same gradualness to your cardio outside of the gym. In your first two weeks, say, decide that you will jog for 15 minutes a time, twice a week. Build that up to 3 times a week for 30 minutes until it's something that you do without having to make a big effort to make yourself go jog. Then start thinking about whether you want to run faster, or whether you want to run for longer, and start considering the distance you're moving.
Going twice a week, you'll want to hit all your muscle groups each time you go, and not go on consecutive days. Therefore, to start, you probably want to pick 1 or 2 exercises targeting each of the major muscle groups: chest, back, arms, shoulders, legs, rear. Since you'll be working all the groups on a given time at the gym, I'd look for exercises which combine multiple different muscle groups at once. For example, if you do squats or lunges with dumbbells, you can alternate that with a shoulder press and thus work the rear, the legs, and the shoulders all together. Start out with just 1 or 2 sets of each, and only increase that when you're comfortable with the exercise and with your current level of commitment to the program.
If you're new to lifting weights, you probably want to start with light weights and focus almost entirely on form. Read through the descriptions of exercises on this site, look at the pictures, watch people at your gym who do them, and don't be too afraid to politely ask someone after they've finished a set if they'd mind telling you whether you're doing something correctly. It can be helpful when you're a beginner (or when you don't have someone to spot you) to start out using a weight machine. Free weights like dumbbells and barbell give you a better workout overall, but machines constrain your motion and make it less likely that you'll overextend yourself or twist something incorrectly. When you start to get an idea of what the strain is supposed to feel like from a given exercise, then you can switch over to free weights and have much more confidence that you're using them properly.