Between his nomination and the hearing, Pompeo has been the subject of a lengthy background check by the FBI and the Office of Government Ethics has vetted him for potential conflicts of interest.
I have no insider information, but typically, nominees meet with Senate committee members and their staff prior to the hearing. I'm assuming that's been happening. On Jan. 11, Pompeo will be formally introduced to the committee prior to testifying and taking questions from the committee during a public hearing. Others may testify in support of Pompeo.
The committee will vote on the nomination in executive session, and if Pompeo receives a majority, Pompeo's nomination will be forwarded to the full Senate. It used to require 60 votes to confirm a nominee, but the Democrats--in their infinite wisdom--changed Senate rules in 2013. Pompeo will only need 51 Senate votes for confirmation. With 52 Republicans in the Senate, Pompeo's confirmation is virtually assured.
Once Pompeo is confirmed, Gov. Brownback will have 5 days to set an election date to replace Pompeo in Congress. The election date must be more than 45 days, but less than 60 days, from the day the vacancy occurs. Pompeo can't be formally confirmed by the Senate until he is formally nominated by President Trump--so sometime after Jan. 20. If Pompeo is confirmed before the end of January, which I think is likely, the election to replace him occur no later than April 1. It could be as early as March 7, if Pompeo were confirmed on Jan. 20, and Brownback scheduled the election in the shortest amount of time possible.
Here's how Pompeo will be replaced.