This is the big post, mostly based on the work of others who went to concerts in Japan before me.

Option #1
The best way to get tickets through official channels is to have someone who lives in Japan buy the tickets. If you have a friend or family living in Japan, you might be able to get official tickets. But the bigger the artist or event, the faster tickets are sold out.

Option #2: Yahoo Auctions
Tons of people sell their tickets on Yahoo Auctions. Some because they can't go on that day, some because they want make a profit or some that got them through the fan club lottery and they can't go or are bad seats. So you could bid on tickets here and win them like on Ebay, but YA has a particular system when the ending time of the auctions comes nearer. When in the last hour, some makes another bid, another hour is added. This is done to counter people who do a higher bid in the last seconds of an auction and they win. This makes it a little bit more fair and actually is good for the seller as he might get a higher final bid.

There is still another big problem, about 99% (read: all) of the sellers on the Japanese Yahoo Auctions site do not ship internationally. Again, having someone you know in Japan helps in this situation again, but for people who don't, there is still a solution: using a third party bidding service.

A third party bidding/shopping service is a website/company who are situated in Japan and who will bid for you on auctions, buy stuff from online Japanese web shops or buy stuff for you from a shop in the street. They also sometimes help you by translating a product page or check if it is actually in stock to buy. Some even have automated auction bidding services through their website, that bids for you on an auction. Of course, there's a catch, such services come with a price, which can be 10-30% + the extra shipping from Japan to your country. But there is really no other option and you're going to be in Japan soon, or don't have anybody in Japan that you know, this is a good option, even if it comes a little pricier.

Option #3: Reseller shops
If Yahoo Auction is not an option either, you still have the reseller shops in Japan, which is the easiest option. You wait to buy your tickets until you're in Japan. This might seem risky because you've come such a long way to Japan and you may be afraid there won't be any tickets left. The first time I got my tickets through Yahoo Auctions, but the second time I bought some at the reseller shops, and usually there are quite a few tickets left. Unfortunately, this also comes at a price, as they sell better seats at higher prices. Front row is very expensive (even on YA, prices of 50-100.000yen are not uncommon). But tickets are usually in the 10-50.000yen range. Also, ticket prices may vary greatly as the concert date draws nearer, because they have to sell the ticket anyway or they don't have any profit. But don't count on the price of a certain ticket to drop, cause someone may have bought the ticket before you do.
There are about 4 reseller shops in Tokyo and I suggest checking them all to compare prices and seat location.

Option #4: Scalpers
This may be a last option if you didn't find a ticket you liked in the reseller shops. Usually there are people outside the concert, trying to sell their tickets, again for a higher price. Or you might be able to trade 2 tickets for 1 better ticket. But remember that scalpers are actually illegal and you don't always see them. But if you're lucky, you can find a ticket at the last moment. As these scalpers need to lose their ticket badly, they will drop their price a lot when the concert has already started. But you see, everything comes at a price.

As a final note, the original ticket prices for concerts are always the same for the whole venue, it doesn't matter if it's front row, or you're in the back, the original ticket is fixed...

I will write up some more detailed info about the reseller shops later.
This guide is originally based on the experiences of people from the AHS forum, added with some personal experience.

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Basically there are 4 main reseller shop (that I know of) in Tokyo located in Shinjuku, Harajuku, Shibuya and Ueno. (if there are others, let me know :))

1. Ueno
Easy to find and close to Ueno and Keisei Ueno station. It's right across the street from Keisei Ueno station (which could be where you arrived from Narita Airport if you took the Skyliner, and is at the south entrance of Ueno Park). If you come from Ueno Station, go under the railroad bridge (not the highway bridge), and pass Ameyoko on your left and follow the road further as it curves to the left. You will see Keisei Ueno station and Ueno Park on your right, the reseller shop is somewhere on your left.

2. Harajuku
Also very easy to find, go to Takeshita Dori (the narrow and very busy street with all sorts of special clothing shop). It's right in front of the exit of Harajuku station. Go into the street and about 2/3 through, you will find the reseller shop on the left. They used to be on the second floor of a clothe shop, but they seemed to have moved next too door, downstairs.

3. Shibuya
Just a little bit more difficult but still easy. When you're at Hachiko crossing, the busiest pedestrian crossing in the world. Take the street to the left toward Shibuya 109. When you come at the junction at Shibuya 109, take the left street next to Shibuya 109 and then the second street on the right. The reseller shop is in the middle of this short street.

4. Shinjuku
Not difficult to find but you need to get out of Shinjuku station through the right exit (and Shinjuku station is HUGE). Take the South East exit (look for it on the yellow directions in the station), it has a large stairway going down with a bridge on the right. When you're down, go to the right under the bridge, and immediately into the street to the left next to the bridge. The reseller shop is on the next corner in front of you.

I'll make some maps, to find it easier :)