I think it's a pity no one has responded yet, when so many respond to the utterly inane threads on the front page, so I'll attempt to give you a bit of advice (and maybe putting this back on the front page will get some more responses for you).
First off, as I think anyone will tell you, you've got to get your diet right; without that, all your other efforts will be in vain. I highly suggest taking a look at the articles in the "Meal Plans" news section on the front page of this website to get yourself some good, basic knowledge about eating right for a life-long healthy lifestyle. You need to remember to look at everything you're going to be doing as something that contributes to a lifetime of health, and remember that these changes should be such that you can continue them all your life. To that end, in all the advice I'll give and others hopefully give, I recommend slow, deliberative steps that you can stick with; I find radical change to usually contribute to backsliding, so take your time to really inform yourself. An informed mind is your best friend in this. In terms of food, I'd also recommend reading Michael Pollan's The Omnivore's Dilemma
. I advise that not because it's good for getting diet tips, but because I think it really helps to broaden your understanding of all the different things that go into the human process of creating and eating food, and so I hope would help you think more broadly about the topic of food in general.
As to fitness, my fitness advice here isn't going to be superb but since you're really looking just for tips that's what I'm going to give you. I always recommend to people that the simplest thing they can do to increase their fitness is to begin incorporating exercise into the routine you already have in your life. That can be in addition to adding in a separate exercise routine at a gym (though it seems that's not something you want or are able to do right now), but can also be done without it and still contribute to a healthy life. Basically, what I want you to do is to assess where in the schedule you already have can you incorporate exercise. If you're close enough, walk to work instead of driving or taking public transport. If you're not close enough, get within a mile or a half mile of work or school and then walk the rest of the way. Take stairs instead of elevators. If you drive somewhere, find the farthest parking spot away from the entrance instead of the closest. If you work at a desk job, do your work standing whenever possible. Buy a bike and bike places. These are all things that you can do with minimal change to your daily schedule while still getting huge benefits back from them. They're things that a healthy, conscious life should include anyway; they're things you can do your entire life even if you start a separate exercise routine and fail at sticking to it.
Lastly, in terms of an exercise program you can do without equipment, why not try the One Hundred Push-Ups Challenge?
While I haven't done it myself, I'm thinking of starting it. Hell, let's do it together! That's something you could do without any equipment at all, and still get great benefit from.
I hope some of this helps, and that maybe other people with toss in their expertise (I consider myself an amateur in this area trying to give what little advice I have gleaned and relying on the great advice of the others here who really know their shit).