Disclaimer:  I am not an MD

>How does one calculate the amount of calories needed
>for maintenance and the deficit needed to lose weight?

Here is a general heuristic.

Maintenance calories per day:   15 x bodyweight in pounds

Then you need to reduce by 3500 a week (500 cal per day) to lose 1 pound
per week and 7000 calories per week (1000 calories per day) to lose 2
pounds per week.

Even simpler:  12 x bodyweight in pounds is a good starting point for
weight (fat) loss.  Adjust up or down as needed, but never ever drop below
1000 calories per day.

James at Penn State