When you go to see a club for the first time, chances are you are walked through the entire facility by the sales rep. While they are likely very thorough, your first day should be spent more exploring the equipment. If you have decided to go the route without a personal trainer, you should absolutely start with the machines.
The machines are designed to isolate each muscle group. As you explore, you will find that the devices will have a plaque or sticker showing a diagram of the body and what area(s) you are working with it will be shaded in or coloured. The marking will also contain the name or what area of the body the machine focuses on. After you have become familiar with the machine and its functions, test it out at a very light weight or no weight at all to experience its movement and how it feels in accordance to your body. Generally you will do 1 set of 10 of all the machines in one day for the first week, going to the gym 3 times and dividing them with rest days between each workout day. The following week you increase to 2 sets of 10 keeping the same work out days, and then the following week you will increase to 3 sets of ten, but changing your routine to 4 times a week, with a rest of at least one day between two workout days. The days that are together you will divide up the routine between upper body and lower body. Start light with the weights and test the resistance to the muscle. If it's comfortable, with medium resistance, than continue, but don't go heavy on the first days because the risk of serious pain is possible as you're taking these new muscles out for their first drive.