Your company probably has a third party handle the RSUs for them.
In my case, for example, my company uses Morgan Stanley for my RSUs (and my stock options). I go log in to that website and I can see all of my RSUs and my stock options. When I want to sell, I can go into that same website or just call the customer service number and say, "Please sell all my RSU shares that just vested today."
Many plans will also allow you to go in before the shares even vest and you can ask them to sell all the shares as soon as they vest.
As far as taxes go, in my case Morgan Stanley always withheld for taxes from my proceeds and passed the withholding amounts back to my company and they included those amounts on my W-2.
If they don't withhold for taxes, you'll want to definitely see if you need to send in estimated taxes. The value of the RSUs you receive should be treated as ordinary income I believe (average stock price on the day they vest * number of shares).