I told her that I liked her and I asked her out on a date and she said yes. She smiled when she said yes and she said that she just got out of a previous relationship, then she said yes I will go on a date with you. We work together, hang out after work, I was so nervous to ask her out that I couldn't eat or sleep. I never felt this way about another person before. How can I tell if she likes me the same way? What should I do after the date?

Relax homie you got her to go on a date with you. Play it cool. If she let you know she just got out of a relationship go very slow.

How about slowing down and letting the relationship build at its own pace?

She may not feel as strongly as you do, yet. She may be interested in seeing how the date goes before making any other plans. She just got out of a relationship so don't expect too much too soon or you will end up being a rebound.

As for after the date, take her home and behave like a gentleman. If the date goes well, see if she is open to making plans for another one. Make certain you don't allow your own emotions to cause you to push for more than she is comfortable with.

The most important thing you need to do is stop worrying about everything!
You like her, and that's a great feeling to have, she likes you too else she wouldn't have said yes to the date. And it was good of her to tell you she'd just got out of a serious relationship, as she's being honest with you.
Don't read too much into everything, just take her out on a date, have fun, and after the date ask her if she'd like to meet up again. If she says yes then call her the next day or speak to her at work to arrange something. Once you've got the first date over with, everything else will fall into place easier.