You need to start with something small, simple to automate, and high value. Pull down some sweet, low hanging fruit, and you will be able to sell the process. Show how it saved someone a late night or a weekend call. Then you can expand out from there.
To do automated testing well, you need someone who is a resource and an evangelist, and who has buy in from higher level managements.
Treat your automated test development like any other agile project. Produce completed tests on a regular basis.
Adding from comment: That is more of a management issue. Is the code considered "done" before it is documented? Before it is checked in? Before it includes and passes unit tests?
How you approach this really depends on your role. Are you a peer? If so, show others how it makes your code easier for them to reuse and maintain. Are you a lead? Pick your programmer who has the most code problems and help them add tests to avoid those problems. Are you a boss? Set it as a standard that "the code isn't done until the unit tests are in and passing.