I've done this process for Japan, and I'll explane it as simply as possible.
If your going to mainland Japan, then the process will be expensive, but relatively easy. If your going to be stationed on Okinawa, it will be much harder, and even more expensive, at least $2K-3K more.
So, we will start by assuming you have already dropped your car off in the US with a transporter, and have already PCS's to Japan.
Make sure before you PCS, you have all documents possible that came with the car (owners manual) and registration/title
Once you get to your duty location, go to TMO, you need a Japanese customs clearance letter. They should have examples to help you fill it out. Also, it will need to be typed, so you will need to find an old style type writter, or word processer. hand written applications will be turned away. Once your done typing it, mail it using the Japanese mail system (1 week wait time) USPS will take over 1 month to deliver it, and ship it back to you.
once you have the customs paperwork back (if you did it right when you get on station) your car should be arriving at Yokohama North dock (U.S. Army installation)
Go to a local insurance branch (should be a rep on your new base) and purchase JCI, and personal insurance.
Once you have done this, you can go to your local city hall, and pay for 5 day temp tags (slash plates) (about 750 yen) Be sure to take with you the customs letter, U.S. title/registration, JCI paperwork, Insurance, and ID card and Japanese SOFA drivers license with you.
take the plates to pick up your car at the north dock. and drive it home.
Next you will need to find a weigh station, and weigh your car. Be sure to get a print out of the actual weight of the car. (tip) make it as light as possible. it will determine how much you pay in road tax.
after that, you can schedule an emissions test. (1-2weeks out) This is expensive. 230,000 yen to be exact. $2600 with todays conversion rate and it will need to be in cash. the test will take 2 days to complete, and there is only one place in Japan that does it. Its about 2 miles away from Yokota AB, in the Tama district. ( I lucked out with this since I lived on Yokota) This will take 2 days to complete, they test your car hot, and cold (by letting it sit over night) Attached is a picture of me at the place waiting in line behind a guy with a Sterling Martin.
once you pass (if you do, or can fix it to pass) you are ready to go to the Land office for the final inspection. this is a CLUSTER FUNK of a process. you have to run all over this compound, paying all sorts of little fee's and getting paperwork stamped and signed (have about 40,000 yen at least). Once they actually start testing your car, they will check your exhaust noise level, lights, windshield washers, and dash (CEL). You will need to make sure everything is in tip top shape, no oil leaks, and if you dont already have them, install some side marker lights on the fenders. I used motorcycle lights on mine and double side taped them to the fenders, after the inspection, I removed them since I didnt want to cut into my fenders. Just tuck the wires behind the fender, and place the light right by the gap between the fender and doors. you will be fine.
now for the headlights. if you pull your car up to a wall at night, and the head light pattern looks like this ( ----/ ) you will fail. You will blind oncomming traffic. If it looks like this ( ---- ) you will pass. most HID's nowadays look like that, My USDM lexus lights did, and they passed them. if your car doesn't come with HID, or doesn't look like that, you will need to make them look like this ( \----- ) so hopefully they sold your car in a country that drives on the left, and you can just buy those headlights. otherwise, you will have to have someone modify them for you...AAC lighting, or someone similar might be able to help.
after that, you will get your tags. Heres a pic of my USDM car with Jap tags, and me at the emissions test facility.