How can we open a new, but more importantly, how do we do stuff in that new tab?
Webdriver doesn't add a new WindowHandle for each tab, and only has control of the first tab. So, after selecting a new tab (Control + Tab Number) set .DefaultContent() on the driver to define the visible tab as the one you're going to do work on.
Dim driver = New WebDriver("Firefox", BaseUrl)
' Open new tab - send Control T
Dim body As IWebElement = driver.FindElement(By.TagName("body"))
body.SendKeys(Keys.Control + "t")
' Go to a URL in that tab
driver.GoToUrl("YourURL")
' Assuming you have m tabs open, go to tab n by sending Control + n
body.SendKeys(Keys.Control + n.ToString())
' Now set the visible tab as the drivers default content.
driver.SwitchTo().DefaultContent()