Machines are all well and good, but I'm a fan of all out fitness, not just strength.
If you are as unfit as you say you are, do some running and weight-free exercises first. Just two or three weeks of jogging and swimming and you'll feel great, your body will be ready to hit the gym full force to get maximum benefit.
At the same time, get your diet up to par, I have no idea what you currently eat, but I'm sure you know that an apple is better than a big mac, and lean steak is better than a fatty one. Try to get in some rice or pasta as well.
Finally, onto the fun stuff - The Gym.
If you're just going for general body improvement, most the machines come with instructions and you should try em all at some point.
General rule - Work your legs!, lots of people forget to work their legs, and just work their arms/chest/back. This might be great for looks, but your legs are big mucles, and take up half of your body, so don't neglect them.
Start Small - For your first few times, just do 3 sets of 5 reps. It might sound low and you might think you're better than that, but if you have not exercised for a while then stay slow for a bit, let your body get used to it, after a week or two you can increase.
Back to the importance of non-weight exercise - You can get as strong as you like, if you don't do aerobic things like running, riding, skipping, and so on, then all that muscle will still have a layer of flab over it. Sure you'll be healthy and strong (and that is most important), but no one will be able to see it! (and that's important too
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The last point is - DO NO OVERWORK! You might be enthusiastic to gym every day, but your poor body can't deal with that, and you'll have slower gains than if you gave it time to regenerate. If you really need to work every day divide your muscle groups - on one day work one set, then another set the next day and so on.
For the next few months, perfect your diet and work on the running/swimming/skipping, it'll improve your heart, work off some flab, and improve your endurace a tad.
Easy home exercises to do are press ups, chin ups, squats, and the various ab exercises (crunches, sit ups, diagonal crunches, Vs etc)
Press Ups -
Lay face down on the floor, legs straight, placing your hands directly beneath your shoulders, and your toes on the ground, push yourself up. Keep your back straight, lower yourself til you are just off the ground (when your nose hits the floor) and push up again.
Variations include putting your hands further out to the side, or putting them close together (form a diamond between your thumbs and forefingers, your nose should touch the ground inside the diamond)
You can put bricks or books under your hands so you can lower your body further.
Chins are easy - Set up a bar at full stretch height above your head, you can improvise with rafters, or you can buy a bar from a sports store - they can either be screwed in or some jam inside doorframes.
Hold onto the bar/rafter/etc with arms shoulder width apart, cross your legs and pull up, then slowly down, and back up again.
They can be done with both over-hand and under-hand grips, each type working a different group of muscles.
Squats - Stand with legs shoulder width apart, back straight (to keep your back straight you can cross your arms behind your back, or place a broom handle over your shoulders.) Squat down slowly, raise up slowly. Easy.
With all of those exercises, eventually you will be too strong and your own body weight will be too much, you can buy weight vests and the like, or you can improvise by filling a hiking bag with whatever and wearing that to add weight - Make sure you wear it properly, otherwise you might strain your lower back.
