What is the process to switch from National Guard to active duty?

Your AC recruiter signs a DD 368, that needs to be approved by your state G1. That step could take 3-6 months. Once approved, you have 180 days to get a contract signed and send a copy to state G1. That AC contract could take 2-4 months to complete.
Then you also send state G1 your assignment orders after that.
If you are less than 12 months from ETS, then just ETS and enlist AC.

Process is simple, if long.
You talk your COC first, convince them of your wish to go AD.
Then go talk to an AD recruiter and he/she will fill out the necessary paperwork. The competent ones will have all that faxed to your NG command.
Waiting for a response could take a bit. IF you can and if you know the command steps, you can expedite this by hand walking it all the way through. Once it is signed off on, go back to your AD recruiter and you are then free to reenlist AD and carry on with your career.

It can take as little as a week or as long as... six plus months. It really depends on how many layers there are and how convoluted things are. Some are reluctant to release but ultimately do so.

I got my 638 signed to go from the Guard to the Reserve in a week but I had a very short chain of command (I also walked it through as a Field Grade Officer). How long it takes depends on how many layers are between you and the state HQ and how responsive your Chain of Command is.

Good Luck