For significant weight loss, how many more calories should one burn in a day more than they take in?

You don't specify a time frame. That is the determining factor. If you burn 1000 more than you take in a day you should lose a healthy 2 pounds a week or so.

I want to lose 30 pounds in 3 months. PREFERABLY.

Its possible but it is going to depend on your metabolism and dedication. 1500 calories a day is a good target. 3 pounds a week is hard to maintain, but not impossible.

If you lose it too fast you'll put it all back on again and then some. It's pretty much the problem with yo yo diets. Basically by losing weight slowly you 'trick' your body into believing your new weight is the right weight. We have an internal measure of 'our' weight which the body tries to maintain.

So if you were 60kg and put on 3kg the body would adjust it's metabolism to get back to 60kg, same for if you lost it. It is how people don't change shape every time they eat a massive dinner or skip a meal.

Well in truth its about a hundred times more comlicated than that and it's not all understood yet, but it is one of the reasons you can't rush this process. You'll just end up cheating yourself in the long run.

Here is an interesting (open acess) paper detailing some of the biochemical pathwyas involved in weight maintenance.
http://www.ama-med.org.ar/obesidad/R...al_Energia.pdf

I don't understand how 2 pounds is good but three pounds in bad...

LOOK UP A WEIGHT LOSS CALCULATOR ON GOOGLE. Sorry I don't have the website saved on my laptop favs! The calculator Basically computes your BMI and age into what is the 100% maintenance level for your current weight and provides calorie deficits in increments of 10% 20% 30%... The higher the deficit the quicker you will lose... In the beginning its easy to lose 10 pounds but then it will level off and totally depend on your calorie deficit and with motivation and not slipping, you will lose 2 pounds a week if you are lucky. But Hey that's 40 pounds lost in only 6 months

If you honestly want to lose weight then exercise.

Its seriously hard eating just 1500 calories per day, especially if you work hard!

The tip is, eat what you want in moderation and exercise very hard. Run 5-6 days every week. You know you've worked your body hard if your out of breathe, if your very sweaty and boiling hot.

All these diets of course work, but very slowly. You didn't put weight on quickly and you'll certainly won't lose weight quickly using a diet.

Good luck and report back

Pete