Shopping in Japan can be a very different experience to other countries. While superficially similar the level of service, choice of goods and type of shops is somewhat unique.
Differences to Western shops
Shopping in Japan works pretty much like anywhere else; pick up the thing you want to buy, take it to the checkout and pay. There are a few differences you should be aware of though.
Shops with more than one floor usually require you to pay for everything on each floor before moving on to another. So, if you find an item on the 1st floor that you want you have to pay for it on that floor, before going up to the 2nd floor.
In the west when you buy a new product it often comes shrink wrapped in plastic and completely un-opened. In Japan when buying items like electrical goods the sales clerk may open the box in front of you. The reason for this is both to check the contents with you and to stamp the warranty card with the date and name of the shop. Don't worry, it's all brand new and quite normal.
Japanese sizes tend to be smaller than western ones. An XL t-shirt is more like a European/US L size, for example. If you want to buy clothes figure out your size in metric first if you don't know already, or make sure you try things on.
Many shops have an umbrella stand by the door which appears when it starts to rain. Others have a plastic bag dispenser that you insert your folded up umbrella in. The bag covers the umbrella and catches any drops. When you leave the shop there is a bin to discard the bag in.
Similarities to Western shops
Changing rooms work the same way as western shops. Just ask a shop assistant if you can use one. Often one will be waiting by the room, or if not just stand by it and wave until someone comes over. You might be given a token with the number of items you are taking in printed on it, which you hand back when you come out.
Baskets, bags and trolleys
Many shops provide little baskets to put your goods in. Supermarkets provide trolleys sometimes too. Some clothing shops provide bags as well, which are often transparent. You can put the clothes you want to buy in the bag before taking them to the counter. To carry your shopping home you will be provided with paper or plastic bags. The paper bags are treated so that they don't disintegrate in the rain.