newbie, working with free weights, either the barbell or dumbbells, is going to be the best way to get stronger. That said, you'll want to stick with compound exercises that work a lot of muscles all at once. Good examples are the Squat, Deadlift, Pull-up (or Chin-Up), and Bench Presses. Other than the deadlift, all of the exercises are relatively simple to learn. All of them recruit a large group of muscles to do the work. The are all decent exercises for beginners who want to improve their strength initially.
When you look around your gym, look for a large rack with pins or hooks on each side of the rack that holds a barbell. You may see someone doing squats in them (or bicep curls, unfortunately). This is the squat rack, and it should be where you spend most of your time in the gym, at least in the beginning. Hopefully, your gym will have the racks with the pull-up bar on the top so you won't have to move until you are going to do presses.
It should be fairly obvious where you are going to bench press. Just look for the bench the with all the kids wearing wifebeaters are yelling out "IT'S ALL YOU DUDE, COME ON PUSH IT!!!" while attemping to hit 120 for one. Just kidding, but it's still fairly obvious where to do bench presses. It's just a long bench with a bar on pins above it. Lie down on the bench, lift the bar up, lower it down to your chest and push it back up.
I happen to have the link to a great article on learning (and perfecting) the deadlift. If you don't do this ONE exercise, you're gonna short change your results by a hefty chunk. It would be wise to learn this move.
You'll also want to research post-workout nutrition on your own accord, as I feel my post is getting a bit drawn out. Getting the proper nutrients in your body after your workout is key to great results as well, so I thought I would mention it.
Anyway, hope that helps you out a bit. Good Luck!