Oh I remember that first day on my own with the 2 girls like it was yesterday! You just have to take each minute as it comes. Don't worry too much about housework or anything like that. Just attend to your needs and your girls needs.
Our girls are the same age apart (I have a August 06 DD & a May 08 DD )

How do people do this? How do you make sure each kid gets what they want/need when they are both screaming at the top of their lungs?
Think about who needs the attention first. If they're both screaming, and it's because they're both hungry, grab something to eat quickly for DD1 then feed DD2. Make sure you have a lunchbox in the fridge organised first thing in the morning for DD1. It will make it a lot easier for meal times. Grab a book while you're feeding DD2 to read to DD1, or put on a dvd. Whatever she is interested in.