I've mentioned buying toys and books on amazon.co.jp. So here are some instructions for paying at a convenience store.
First of all, you should know that you can get most of the info in English if you look for the "Display this information in English" link on the right of the page. This can be a little tricky to spot, but it is there. Search for what you want and then put it in your cart and checkout. Go through the steps and input your address etc. When it comes to the payment method, choose pay at a convenience store. NOTE: If it is a non-amazon (or marketplace) seller then you can't use this option.
First, you will get an order confirmation email. The next is probably the "payment number." Scroll down until you see your email address, a long number and the amount due. Write down the long number and take it to any convenience store. In my experience Lawson's red kiosks are the easiest to use, but for us Family Mart is closest. Here are some instructions for Family Mart.
Here is the machine:
Just touch the screen to begin. This is the section for paying on Amazon on the first page:
Go to the next page by pushing on the down arrow. Look for the Amazon logo
The first page you need to input your payment number.
On the next page you need to enter 888 for some reason.
Then push the confirm button "確認” (A good Kanji to learn by the way) on the bottom left.
The machine prints out a ticket that you then take to the counter to pay.
I hope this helps. As soon as you pay they send your package- we have got ours the very next day sometimes.
Here is a useful post from Surviving in Japan about vocab for ordering online.