Why can't I use arrow keys in terminal on Debian 6? (nonroot)

You appear to have /bin/sh as the login shell of your non-root user, and /bin/sh point to dash. Dash is a shell designed to execute shell scripts that stick to standard constructs with low resource consumption. The alternative is bash, which has more programming features and interactive features such as command line history and completion, at the cost of using more memory and being slightly slower.

Change your login shell to a good interactive shell. On the command line, run

chsh -s /bin/zsh

(You can use /bin/bash if you prefer.) Configure your user management program to use that different shell as the default login shell for new users (by default, the usual command-line program adduser uses /bin/bash).