How do you install .deb files in OSX?

You don't.

Debian software packages are binary software packages for Linux. They are dependent on another operating system, and you need to use the Debian package manager (which OS X doesn't provide).

You can, if you want, use MacPorts or FINK instead. Most of the Linux packages available as RPMs or Debian packages are also available for OS X via MacPorts and FINK.

Can you give some more detail of what you were doing in fink? For instance, what you were trying to install, what command you used to install, what happened, and how you found the .deb files but discovered that the package was not installed.

fink makes a debian (deb) file AND installs the package by default, if you issued a command like

fink install packagename

where "packagename" is the name of the specific package you want to install.

To see if it is indeed installed, type

fink list packagename

and you should see the letter i in a column before the name of the package.