Whenever I go to the gym I try to focus on two muscle groups at a time: back and biceps, chest and triceps, or legs and whatever else I feel like doing that day (oh, and don't forget to do shoulders occasionally too). If you look at most gym equipment you'll see diagrams highlighting which muscle groups each machine focuses on. You'll generally notice that equipment that works out the chest also works out the triceps, same with back and biceps; so if you get stuck, just look at those diagrams.
With each workout, you'll want to make the weight heavy enough so you can do at least eight reps, but ideally you should struggle to complete twelve. That way, as you get stronger, you always have a benchmark on how heavy you should be setting your weights. What I've learnt is that if you're always lifting heavy weights with low reps, you'll build muscle faster; and if you're lifting moderate/light weights with high reps, you'll tone your muscles (or at least maintain your current muscle mass). Make sure you're using the equipment correctly though, you don't want to hurt yourself by using the equipment the wrong way. You can book a time with a personal trainer (PT) to show you how to use the equipment if you want, or just ask the manager while they're there if they have time to show you. Most of the equipment is pretty straightforward, but again, if in doubt: look at the diagrams on the machines.
So you'll want to do eight-twelve reps, take a short break (about 30 seconds), and then do another eight-twelve reps (by the way, each collection of reps is called a set). You should do three sets on each machine. I mix it up by doing a set on one machine, then going to a separate machine that works the other muscle group, doing a set on that, and then returning to the first machine again, and repeating the process until I've done three sets on both. I do that because I want to make the most of my time at the gym and get out of there quicker. But be aware that if it's busy at the gym then someone might take your machine by the time you come back to it, so you may find it better to stick to one machine until you've completed all three sets.
Cardio is good for weight loss, but lifting heavy weights burns fat much faster (plus you gain muscle at the same time: win/win). But you should still do cardio to build up your endurance regardless. At the moment I'm only running for about a kilometer when I first get to the gym, and then I do my other workouts until I've run out of machines to use, and then I'm back on the treadmill (if I have any energy left) and run for as long as I can be bothered. I've been aiming for five kilometers but I'll have to work back up to that because I've been a lazy couch potato lately.
To keep it simple: when you get to the gym just run for a bit until your heart rate is up and you're starting to sweat, and then get onto the machines. You could use the bikes or rowing machines if you'd prefer, or do any other cardio that's available (and not frowned upon) at your local gym.
Don't be afraid to try the free weights as well, try doing the same amounts of reps and sets of bicep curls, chest presses, or shoulder presses with barbells and/or dumbbells. Maybe get a PT to show you how to do these correctly if you're unsure. Also have a look what other people in the gym are doing, if it looks like something that's working out the same muscle group you're working on then try to mimic them when the equipment is free. You can start on a lower weight to make sure your form is correct and then try something heavier.
That's all I can think to tell you for now, other than maybe some nutritional advice (avoid sugar as much as you can). Also you shouldn't work out on an empty stomach either unless you're only doing cardio. Drink a protein shake right after your workout when you get home, I find those Magic Bullet blenders are super convenient. Just blend protein powder with frozen bananas and water or whatever you'd prefer.
Remember that pain is good, if you're not hurting after the gym then you'll be unlikely to gain much muscle or burn much fat. Hope this helps and I've haven't missed too much, but feel free to ask me any questions and I'll try to help the best I can.