General questions and examples of SPNEGO over REST via C#, Java, Python ?

I am connecting to a web application that is integrated with Active Directory. The application allows  for  REST operations via SPNEGO.

My understanding is that I should be able to make a REST call using GSSAPI/SPNEGO. First a general question.  My understanding is that the process works like this.

1) User logs into their computer and gets a TGT which is stored somewhere off in memory (I'm a little fuzzy on this, I believe this is how KERBEROS works, and I'm hoping SPNEGO assumes the same)
2) Client tries to make some request like a GET or PUT
3) Website respondes with unauthorized 401 response with an WWW-AUTHENTICATION : NEGOTIATE header.
4) Client responded with a second GET or PUT request adding a Authenticate: NEGOTIATE %token string%
5) Request succeeded and client get proper response


My questions are:
1) Is the above understanding correct?
2) If my goal is to only get the %token string% How would i retrieve that string value to add to the Authenticate: Negotiate header?
    1) In C#/.NET
    2) In Python
    3) In Java