Hello experts PostgreSQL

We have and old server running postgreSQL 7.4 and CentOS 4.4 (pretty old, its been up since about 2005) with its hard drive at about 3% free. We have a new server at hand (Ubuntu 12.04, PostgreSQL isn't installed yet) and I would like to ask your advice on how can we migrate the database from the old with no downtime or minimal downtime as possible.

Any steps on how we can migrate safely and immediately?

Thank you in advance.