Haha, shopping that isn't expensive?
As far as I can tell, Japanese people shop and don't worry about breaking the bank. There are some cheaper places, though.
If you're in Harajuku/Omotesando, there are all sorts of used clothing shops that have clothing that may have been worn once, if at all. You'll notice, though, that the prices will be like this (example, a t-shirt):
There are some that are less expensive, but that's generally it.
For general clothing (and actually good deals on t-shirts and such), Uniqlo is pretty hot. It's pretty trendy and the t-shirts are artsy, and sort of comparable to the Gap. (The Gap costs about 20% more here, BTW.)
Assuming that you're looking for fashionable stuff, though, and that you're young, you're gonna want to stay in the Harajuku/Omotesando/Aoyama area. Department stores are not places to get anything on sale (rather, they're super expensive). But walking the backstreets of the area can be a good idea! You can also check out Daikanyama and head out to Odaiba, both areas with shopping and large malls, respectively. If you go to Shibuya, you will find more of the "kogal" oriented shops (the orange colored girls) but there are some deals, sometimes, in 109 and generally deals on the street as well.