The following text has been taken from Preview Forums on Xbox website.  All the credit goes to Xbox.

• To get started you can just say “Hey Cortana”. You can also launch Cortana from Snap Center in the Guide, or from My Games & Apps.
• Cortana works with headsets. If you don’t have a Kinect just plug in a headset and start using speech on your console. You’ll notice a new microphone icon in the top right corner of Home dashboard which indicates when a microphone is connected and available for use with Cortana.
• Cortana also understands you when you speak naturally, and will recognize commands you’re already familiar with. Just say “Hey Cortana” instead of “Xbox” for commands you already use. For instance you can say “Hey Cortana, go home” in place of “Xbox go home”.

Things To Try

• Launch a game or app by saying “Hey Cortana, open {game/app name}” or something fun like “Hey Cortana, let’s play {game name}”.
• Check on what a friend is up to without pausing your game by saying “Hey Cortana, what is {friend name} up to?”
• Invite a friend to a party with a single phrase by saying “Hey Cortana, invite {friend name} to a party. Search the web with “Hey Cortana, search the web for Xbox One”.

Known issues
It’s early for Cortana on Xbox One and we’ll continue to make improvements and build new features. We’re still tuning Cortana, so please bear with us, and be sure to report issues via Report a problem!

• If Cortana doesn’t hear you the first time, you can usually try saying the phrase again.
• In some cases Cortana won’t recognize the name of any game or app (ie. “Hey Cortana open Netflix”). This is an issue we’re working to address, so please use Report a problem if you encounter it.
• If Cortana says she didn’t hear you right after you say “Hey Cortana”, navigate to Settings > Account > Privacy > App > Speech > Collect Info (accept)” and confirm the setting is checked.
• When Cortana is “Thinking…” sometimes the sounds continue longer than intended. You can open Cortana from Guide or My Games & Apps and then close it again by hitting B button.
• On the first use of “Hey Cortana” after a reboot or crash, Cortana snaps but may display no results.
• You may be unable to use See-It-Say-It in various apps such as Netflix, YouTube, and the Blu-Ray Player app.
• Cortana sometimes needs to spend more time “Warming up…” than she should.
• Sometimes short commands are recognized incorrectly (ie. “Hey Cortana mute”, “Hey Cortana pause”) and initiate a web search instead.
• Sometimes short commands take longer than they should to be recognized (ie. “Hey Cortana mute”, “Hey Cortana pause”). “Hey Cortana snap TV” sometimes launches Movies & TV, rather than TV, until you say “1” or “2”. “Hey Cortana turn off the Xbox” … “Yes” in UK, FR, IT, DE, and ES sometimes gets stuck on the confirmation and fails.

List of Commands
Power – Turn your Xbox on and off
“Hey Cortana, Xbox on” (only with Kinect)
“Hey Cortana, turn off”
“Hey Cortana, restart”
Media controls – Control your media playback
“Hey Cortana, pause the movie”
“Hey Cortana, rewind”
“Hey Cortana, play the next song”
“Hey Cortana, mute”
Audio controls – Control your sound level
“Hey Cortana, volume up”
“Hey Cortana, mute”
Navigation – Getting around on Xbox One
“Hey Cortana, go home”
“Hey Cortana, go back”
“Hey Cortana, show menu”
“Hey Cortana, change view”
“Hey Cortana, switch”
“Hey Cortana, show notifications”
Profile – Sign in, out, and off
“Hey Cortana, sign in”
“Hey Cortana, sign in as John”
“Hey Cortana, sign out”
Friends – Play and chat with friends
“Hey Cortana, is Michael online?”
“Hey Cortana, what’s Amy doing?”
“Hey Cortana, start a party with Ryan”
“Hey Cortana, send a message to Jasmine”
Games & apps – Jump in and have fun
“Hey Cortana, snap friends”
“Hey Cortana, launch settings”
“Hey Cortana, play Forza”
Game captures – Record your awesomeness
“Hey Cortana, take a screenshot”
“Hey Cortana, start broadcast”
“Hey Cortana, record that”
TV & OneGuide – Sit back and enjoy
“Hey Cortana, watch TV”
“Hey Cortana, watch ESPN”
“Hey Cortana, show the OneGuide”
Search – Find what you’re looking for
“Hey Cortana, search the web for news about Xbox One”
“Hey Cortana, search the store for Minecraft”
Help – Get answers
“Hey Cortana, help”
“Hey Cortana, what can I say?”
Places – Get directions
“Hey Cortana, show me a map of 123 Main Street”
“Hey Cortana, how far to the Grand Canyon”
“Hey Cortana, when does Starbucks open?”
“Hey Cortana, find cheap pizza restaurants near me”
Facts – People, places, things, stuff
“Hey Cortana, who is the tallest woman in the world?”
“Hey Cortana, who is the president of Finland?”
“Hey Cortana, what’s the capital of Qatar?”
“Hey Cortana, who won the first Super Bowl?”
“Hey Cortana, how tall is Mount Kilimanjaro?”
“Hey Cortana, how many floors are in the Empire State Building?”
“Hey Cortana, who built the White House?”
“Hey Cortana, who are Tom Hanks’ parents?”
“Hey Cortana, when does Fall begin?”
“Hey Cortana, where was Obama born?”
Tracking – Flights and packages
“Hey Cortana, what time does Alaska 32 depart?”
“Hey Cortana, flight status for Southwest 11?”
“Hey Cortana, what’s the status of Hawaiian flight 21?”
“Hey Cortana, when will my package arrive?”
Sports – Scores, stats, and predictions
“Hey Cortana, when is the next Seahawks game?”
“Hey Cortana, what is the score of the Packers game?”
“Hey Cortana, what’s the Arsenal score?”
“Hey Cortana, who will win the 49ers Cardinals game?”
Show times – Movies and concerts
“Hey Cortana, what are the showtimes for Star Wars?”
“Hey Cortana, what movies are playing near me?”
“Hey Cortana, Daft Punk events near me?”
Finance – Currency conversions and stocks
“Hey Cortana, convert 60 dollars to yen?”
“Hey Cortana, bitcoin exchange rate?”
“Hey Cortana, how much is Costco stock worth?”
“Hey Cortana, what’s the stock market symbol for Ford Motors?”
“Hey Cortana, how are the US markets doing?”
“Hey Cortana, what’s the value of Microsoft stock?”
Math – Calculations and conversions
“Hey Cortana, convert 172 pounds to kilograms”
“Hey Cortana, how many meters in 1 kilometer?”
“Hey Cortana, what’s the value of cos 60?”
“Hey Cortana, what is the square root of 256?”
Dictionary – Define and translate
“Hey Cortana, define delve”
“Hey Cortana, what is the meaning of spartan?”
“Hey Cortana, translate hello to German”
“Hey Cortana, how do you say how are you in French?”
Weather – What’s it like out there?
“Hey Cortana, is it hot in Rio de Janeiro?”
“Hey Cortana, will it rain this weekend?”
“Hey Cortana, do I need an umbrella?”
“Hey Cortana, what’s the weather right now?”