How many calories should a 280 pound woman eat to lose weight?

Use the website appropriately and it will guide you.

If you entered a realistic goal in with your stats, the number MFP provides is your base calories. You will earn additional calories through exercise, but remember, most only eat back a portion of those as MFP tends to overestimate them.

Here's a bit more help on how to enter new goals...

Click Goals > Change Goals > Guided, Continue, enter in your accurate information and realistic goal weight, and click Update Profile. MFP will give you good information on how many calories you should eat each day to safely lose weight. Good luck!

Direct Link: http://www.myfitnesspal.com/account/my_goals
BMI Calculator: http://www.myfitnesspal.com/tools/bmi-calculator
BMR Calculator: http://www.myfitnesspal.com/tools/bmr-calculator

Yup, use the tools and make sure you accurately judge your activity level.

I would suggest some reading for better understanding.
http://community.myfitnesspal.com/en/discussion/1235566/so-youre-new-here/p1

http://community.myfitnesspal.com/en/discussion/1080242/a-guide-to-get-you-started-on-your-path-to-sexypants/p1

http://community.myfitnesspal.com/en/discussion/840082

And a group to check out
http://community.myfitnesspal.com/en/group/10118-eat-train-progress
(read the stickies)