Woah!
Ok, first of all, i second everything Blood Hound said. Absolutely. And am similarly shocked by bikenotes recommendations.
Communicate and do some introspection and figure out what you want and what your girlfriend wants. Create a safe space with open communication where you can both share your feelings, needs, wants, fantasies, etc. without fear, shame or judgment. "Dominant" and 'submissive" have as many meanings as there are people who identify with those labels so you have to figure out where each of you are and get on the same page!
Figure out where limits and interests are for both of you and get some safety basics in place for you both!
Next, please, please, please educate yourself before you engage in ANY play, let alone the kind of "edge" play recommended by bikenotes. The activities she mentions are things people do but are so very far from the only things or even the most common and, as Blood Hound points out, have very little to do, in and of themselves, with being "Dominant". ANY BDSM activity has risks and there is rarely one right way to do anything but there are ALWAYS many wrong ways. Educate yourself and learn how to safely and properly do anything you are interested in, preferably with the instruction of someone very skilled and experienced! At the very least, exhaustive reading and research is required. And your girlfriend needs to be fully educated and aware of any and all risks before you begin as well. This is the only way truly informed consent can be given! There are ALWAYS physical and mental and emotional risks involved, and everyone involved needs to be fully aware.
If you purchase anything at this stage in the game, look at some good books on BDSM. There are 4 books i always recommend:
1. The New Topping Book by Dosse Easton and Janet Hardy available on Amazon
Here
2. The New Bottoming Book by Dosse Easton and Janet Hardy available on Amazon
Here
3. SM 101 by Jay Wiseman available on Amazon
Here
4. Screw the Roses, Send Me the Thorns by Phillip Miller and Molly Devon available on Amazon
Here
All 4 of these used to be available on Eden but i can't find them anymore.
Anyway, if you want someone else to chat with on the topic, i'm also available by private message.