It's up to the community to decide on criteria for a witness, but I would personally expect more real word reputation, not just in trading (e.g. if you are a google, you are OK with me

).
One way to become a witness is as follows:
1. Run the witness code on your server
https://github.com/byteball/byteball-witness. To be considered seriously, you need to run it on a server that is well connected and always online. Running this code alone won't make you a witness automatically, you'll just periodically post your units to the database (and spend your bytes by doing this).
2. Campaign here and elsewhere trying to persuade everybody that you would be a better witness than somebody else and they should change their witness list by replacing some other witness address with yours.
I'm fascinated by this new tech, wow!

@tonych:
Are you already accepting applications for witnesses? I would love to be part of this project. I have no problem to reveal my true identity. I'm here since 2013 and did a lot of trading with good reputation. Not only digital but also physical goods, so my postal address is also known to several members. Please contact me by PM if you have any further questions.
As a witness, should I run the client on a vps or is a local pc sufficient?