How can I retake the ASVAB?

Step one- google the nearest military installation
step two- locate their education office
Step three- call them, or walk in and ask about retaking the ASVAB (its called something else for Service members but they will know what you mean)
Step four- let them give you a practice test as well as assign you a tutor (free)
Step five- meet with your tutor on a regular basis
Step six- actually retake the ASVAB

I would recommend that you first work with your Training and Ops NCOIC first.

I was in the USAR (AGR) when I retook my ASVAB. I recommend you purchase and ASVAB study book with pretests. Once you complete the pre-test you'll know your good areas and the bad areas.
Research the specific test subjects that combine & makeup the MOS you're considering.
Then all you have to do is study these subjects you scored the lowest on (because the subjects you did well on don't need any more studying).
When I came back from my second back to back tour in Iraq, in 2008, I was able to make an appointment at a National Guard facility for my ASVAB retake.
My original GT score was 97 (this was way back in 1995 when I was in high school).
My updated ASVAB score came out to 111!
Good luck!

I was AD from 2010 to 2014. So this may have changed. But I believe it was 2 years in service before you were allowed to retake. But I'm sure there are unit regs, post regs, commander regs on it. Best bet would probably be to just go ask a recruiter and skip the middle man.