Hanoi has little in the way of high-end shopping, but there are many small shops selling local crafts and manufactured items. The "Old Quarter", also known as "36 Streets", is a good place to explore as well as shop. The "36 Streets" name for the district comes from the thirteenth century, when Hanoi's 36 guilds each had their own street. This is why, if you translate the street names of this area, you get "Silk Street", "Silver Street" and so on. You can't rely on the old guild separations any more, but you can still find plenty of silk, silver, lacquer and other crafts in the Old Quarter.
Lacquer-ware and carved stone - some of the typical handicrafts of Vietnam
If local handicrafts is what you're after, then 'the' place to go is Craft Link. Craft Link is a Vietnam based non-profit organization that acts in the interests of traditional craft producers. Products in the shops are purchased directly from the craftsmen and profits are used to fund development activities such as business training, product development and marketing. Craft Link is a member of the International Fair Trade Association. For more information see the Craft Link web site.
Craft Link is just outside of the Temple of Literature. As you exit through the front entrance of the Temple, turn left. At the first intersection, cross the street and turn left again. The Craft Link shops are about one block up.
Note that unlike many small shops, Craft Link takes all major credit cards.