How do you get into Red's Shop on Animal Crossing City Folks?

First go to Redd's shop and listen to the dialog.

Then go back to your town and talk to your neighbors

(it may take some time for your neighbors to mention the shop, maybe a week). When they do mention it, pretend you do not know and have never heard of Redd's shop, including when you answer questions. Once they ask you if they can send you the invite, say yes (remember that it costs 3,000 bells for a membership).

The next day the invite should be in the mail. Go back to Redd's shop with it and he will let you in! :D