You'll face away from the anchor, being "inside" the straps so to speak.
Its kind of like doing a pushup in mid air is the best way to explain it. I do believe they cover the Chest Press in the Video Library here on the site.
The only difference between the standard Chest Press and the Deep Chest Press is the angle you are at. So your feet will want to be nearly or literally be touching the door when you do them.
It's not seriously demanding but try a couple out before you get constantly going on them, to make sure you can handle doing them without your muscles wanting to give out on you. I just know the first time I did it, after about 5, I fell down and rubbed my knee on the carpet that I just skinned the day before hiking... 