Good for you Poll 
Firstly do you have any medical conditions?
Any weak joints etc?
Are you pregnant?
As a bog standard beginner gym visit. I'd familiarise yourself with the machines.
Ideally go with DH - you don't have to even go dressed for the gym, just walk through with him and he can show you it all.
It's easy to feel intimidated, but really, all of those people will end up sweaty and not caring what's going on around them.
Even if there isn't a full induction - someone will be able to show you how to set the weights. It's usually a case of a stack of rectangular metal plates with holes in and you move the pin up or down to make the weight heavier or lighter.
There are generally diagrams on them to show which muscle groups you're working.
The running machines etc are cardio - fat burning and raises your heart rate.
You could start off by doing between 6-12 minutes on these.
If you just press 'quick start' it will start the machine, you can then press the 'level' or 'speed' to increase the intensity.
E.g. the cross trainer.
You stand on it.
Get comfy.
Press quick start
Start moving
Get into a rhythm
After a couple of minutes you can press level/up/increase and it will make it slightly more difficult to do the movements.
I started doing: (many many years ago so forgive me if I'm rusty
)
12 mins on the treadmill, 6 fast walk, 6 running.
12 mins cross trainer
Sets of weights: set of 3 lots of decreasing 12
Eg leg curl.
Sit on the machine,
Adjust the pin at the side so your body is in the correct position as shown on the diagram.
Check the pile of metal kg weights is low enough for now.
Do 12 leg curls.
Wait, or stand and stretch
Do 10 more, repeat.
Do 8.
After a time, you'll increase the weight you're pushing against for the last set of reps, but that's for once you're more familiar.
Then back to cardio,
Maybe 8-10 mins on the rower.
Make sure you do some stretching to warm up and don't forget to cool down.