1) Yes, you can drive in Japan.
2) Get an international driving permit before coming to Japan.
3) If you view yourself as a resident of Japan, you must obtain a Japanese driving license.
A climber without a car is like a fish without gills. A climber must have some wheels, lest he's willing to suffocate.
People tend to discourage you from driving in Japan. Don't listen to the naysayers. Sure, if you cannot read Japanese, it's a bit harder to drive in Japan than in other foreign countries, but not massively so. A good co-driver or a carefully preplanned route helps. And it's not hard getting used to drive on the other side of the road if that applies to you.
The motorways are convenient and in excellent condition, but charges the highest tolls in the world. Some of them are not much in the way of expressways either. The Tokyo-Nagoya expressway is a particularly perma-congested example; fortunately the 2nd Tokyo-Nagoya expressway, running a few kilometer north of the first is under construction. (And yippie! It will have an intersection in Shinshiro-city, cutting the time to get from Nagoya to Horai in half, I would guess.)
For short-time visitors it make sense to rent a car. Car-rental is a relatively painless process, and can be quite cheap as well, especially if you rent a “kei-jiitousha” or “kei-car”, i.e. a car with an engine having maximum displacement less than 660 cc. Some low-price car rentals will not let you rent a car if you don't have a Japanese driving permit.
Unless you “reside” in Japan you can drive freely using an international driving permit. Get your international license well in advance. In Sweden it only takes a few days to get one, you may not be so lucky.
If you are a “resident” a Japanese drivers license must be obtained. How to go about this depends on where you got your license. If you have an American (North- or South-) license I pity you. Australia and most western European countries have a bilateral agreement with Japan which makes it relatively painless to get a Japanese license. Google the process.
People using an international drivers license who are resident in Japan can be subject to arrest. What is then a “resident”?, you may ask. Well, exactly what constitutes the boundary between “resident” and “not resident” is not clear. Simply put that is for the police to know and for you to find out. Anyway, driving without a valid permit is a serious crime: don't even think about it.
Don't go to a driving test center to transfer your license or to do the tests without either speaking some rudimentary Japanese, or bringing an interpreter. Count on having to spend most of the day on the test center.
If you buy a car from a retailer, have them do the paper work for transfer of ownership and parking permit. They should be able to do that for a nominal fee, which is well worth paying, regardless of what the fee might be. If you're buying your car privately — like I did — you have to do this yourself. The transfer of ownership was quite quick and painless, but to correctly fill out the forms for the parking permit tested my skills and patience to the limit.
Funny enough you don't need a stamp to transfer ownership, as long as you show up in person, but I needed one to get the parking permit.
It might be a bit of a pain to do all the necessary paperwork, and you shouldn't be surprised if the parking is way more expensive than the car, but the freedom of having your own car is well worth the price of admission. Good luck!