While the new iPad doesn't include Apple's Siri virtual assistant -- probably for a number of reasons -- it does include the speech-to-text Dictation feature. However, Dictation may not be enabled by default, and if it's not, it's not at all obvious where to go looking for it.
The settings to turn on Dictation are a little hard to find. Here's what to do:
Like Siri, Dictation is a server-side service that transmits your voice to Apple's datacenter where it's processed and the text is returned. Properly figuring out human speech isn't easy, and it takes the power and access to millions of voice samples that, currently, only a data center can provide.
Once you've enabled Dictation, a microphone key will appear on your iPad keyboard. (Note: it won't always appear on specialized keyboards, for example, it won't appear if you're entering in a website address URL, but it will appear on any keyboards meant of standard text entry.)
Try to speak at a steady pace, and enunciate as clearly as you can. If Dictation gets confused about any of the words you speak, it will underline them in blue on the screen. If the word is incorrect, tap it to get a popup menu with alternatives. Tap an alternative to switch to it. You can also simply edit voice dictation text like any other text.