A couple things to remember before getting started:
Wear gloves. Cement will dry out your hands like nothing else.
Wear eye goggles. Cement will dry out your eyes like nothing else.
1. The old hoe and wheelbarrow method: Mixing up a batch of concrete with a hoe and wheelbarrow is pretty simple. You need a hoe and a wheelbarrow, and that's it. Dump a bag of cement in the wheelbarrow, add the amount of water recommended on the bag, and get to mixing.
2. The drill, paddle, and bucket method: You need to rent a heavy-duty drill for this one, and you'll also need a paddle and bucket. I've mixed concrete a few different ways, and this has been by far the fastest. Fill a bucket a little less than halfway with cement from the bag. Add a little water and start the drill in the bottom. Don't add too much water right away or it'll splash everywhere. You'll know the concrete is ready when it starts to swirl pretty evenly, like this:
It's easier to do than using the hoe and wheelbarrow, and actually faster than most mixers you can rent.
But like I said, don't resist the urge if you want to hitch that big mixer to the back of your truck and take it home for a day of big-time cement/concrete mixing. If you've got a whole driveway to pour, you'll need it. There's nothing like the thrill of using real heavy machinery to do a job, whatever it is. And there's nothing like cleaning that heavy machinery before bringing it back to the rental house. They'll charge you otherwise.