How much you should do is going to depend entirely on your body. What you can handle, and what it takes to help you lose weight. What you can handle can change as you become more fit.
When I started out, 30 minutes was pushing it for me. Now, I do between 1 and 1 1/2 hours each day.
As far as ways to do it without taking a lot of time...
Do you get a lunch hour? I've jogged/walked on my lunch hour. I just take workout clothes and you can wash up in the bathroom afterward. Do a simple pony tail if you can get by with it, or go prepared with a hairdryer and shampoo if necessary. Eat lunch at your desk.
Do you work close to home? Bike to work. If not, take the bike and park farther away from the office and bike on in.
More than a one story building? Have fun on the stairs.
Do you sit down to TV in the evening? Stand up to it. Grab some weights and march in place, or get an exercise step and step up and down with weights. Or...hoola hoop anyone?

It's easy after you get the hang of it. Try finding a weighted one. No hand weights, use a couple bottles of water. Leg weights are also a good investment.
If you spend 15 minutes in the morning, 15 at night and put in 30 at lunch, you've got a full hour of exercise in every day and it doesn't really cut into your day much that you'll notice a loss of time.
Add to that hour the simple daily moves that help you shed more pounds...
Park farthest from all doors.
Take shopping carts back into the store.
Take the steps, not the escalator/elevator.
Pace while on the phone, rather than sit.
Play with the kids at the park, or in the front yard...wherever. But get in there and play hard. Act like a kid again.
Take the dog for a walk rather than put him in the fenced yard.
Or try what I'm doing while I type this...replace your chair (home and work) with a body ball and just...sit on it.