First, open a terminal window (Applications->Accessories->Terminal). Then add the repository's key to your system's list of trusted APT keys by copy and pasting the following:

wget -q http://wine.budgetdedicated.com/apt/387EE263.gpg -O- | sudo apt-key add -

Next, add the repository to your system's list of APT sources:

For Ubuntu Hardy (8.04):

sudo wget http://wine.budgetdedicated.com/apt/sources.list.d/hardy.list -O /etc/apt/sources.list.d/winehq.list

For Debian Etch (4.0):

sudo wget http://wine.budgetdedicated.com/apt/sources.list.d/etch.list -O /etc/apt/sources.list.d/winehq.list

Then update APT's package information by running 'sudo apt-get update'.

Now you can install Wine by clicking this link. Alternatively, you can install by going to Applications->Add/Remove and searching for Wine.