How do I lose weight with my new calorie intake goal?

If you told MFP that your goal was weight loss when you setup your profile, then it set your calorie goal with that in mind. You can eat right up to your goal and still lose weight (assumimg that everything you've inputted is accurate and you don't have any medical conditions that would mess with the calculations).

Total Daily Energy Expenditure - it's the total calorie burn per day with all activity included.

TDEE might confuse you, so a bit of an explanation.
There are 2 ways to approach this.

The MFP way. Figure out your base metabolic rate (BMR) and adjust for your normal (non exercise) activity to get NEAT (non exercise active thermosomethingoranother), which is the amount of calories you burn in a day without exercising (brushing your teeth walking to work, walking around at work). You make this adjustment in MFP by picking an appropriate activity level (I'm sedentary). Then you deduct from this the amount of calories needed to lose your target weight loss (500 per lb per week). If you exercise, you add those calories back and eat them as well (adjusted down somewhat for inaccuracies in estimating the exercise burn, so eat back 50-75%). Note that even if you tell MFP what your exercise plans are, it does not include it in the calculation.

TDEE is your total daily energy expenditure and is, essentially, the same thing but it includes exercise so it gives you a higher calorie number then MFP does, but it includes your exercise calories so you don't eat them back. Again, you eat under this number to lose weight (still 500 calories per 1 lb per week).

Both are correct and based on the same math.

Which to use is your choice.

But, in my opinion, TDEE is useful when you have a regimented weekly workout routine that is consistent and you are sure of the calorie burn (based on chest strap, months of experience etc.)

MFP is better if you don't have the regimented exercise routine and exercise periodically. I use my treadmill for 30 mins every weekday, but may use it when watching hockey at night, may use it on the weekends, or may do an outside activity (trying to snowshoe), and I'm trying to lift weights at home but finding I really dislike it and am not doing it consistently. For me, the basic MFP system works better. Plus I know 30 minutes on the treadmill more than covers a glass of wine in the evening that I hadn't allowed for otherwise.