How long does it usually take for a DD 368 to get approved for a soldier going from the Reserve component to active duty?

This all varies on the individuals unit. Anywhere from a few weeks to a few months.

I am currently in the process of going from the guard to the active side. My paperwork as been in for almost a month and is up to the G1 of my state. In the next few weeks I should be released. Hope this helps

It took 4 months for mine to be approved. It takes longer for Officers I think because each BN CDR has to explain why we are loosing each officer. For Enlisted, it's probably a 2-3 month turn around. Just keep checking with your unit.