For discussion of card benefits, see the master thread in the United forum:
Introducing the all-new MileagePlus® Explorer Card
How do I get the 50K offer?
Follow these steps:
Clear all cookies/history from your browser
Log into your United account and click on the 30k banner
Paste or click on this link:
https://www.theexplorercard.com/UMPC...6P&REFERID=TEC
You should get a "please wait while we prepare your application" page, and then an application with your UA FF# and address pre-filled. (You will NOT see the 50k landing page.) If you get a "Try Again" page, go back and repeat the steps. You need to be logged in AND click on the 30k banner to get the application to load.
[source: post 1654 by Spacetime17, with minor edits]
Note: In addition to the directions above, there is a different link that may work for some applicants:
http://unitedexplorercard.com/my50K
The 50K offer is also available at Chase Branch offices.
How much do I have to spend to earn the signup bonus?
The spend requirement is $2000. Not all offers include the $50 statement credit, but some have reported success when sending a Secure Message.
My math says a 50K offer. Where do the extra points figure in? The extra 5000 points comes from adding an authorized user after you have been approved for the card
Is there a business card?
Yes, and Flyertalk has thread devoted to the business card, as well.
Link is here: United business card: 50k+10k united miles
Can I apply for this card and earn the bonus after doing so previously?
See the wiki and related discussion in Applying for Chase Credit Cards [Consolidated].