How to save the state of a Ubuntu install? (get a snapshot)

The only all-in-one solution I know of is a third-party application TimeShift. It's most comparable to system restore on Windows and time machine on Mac OS X.

TimeShift is a system restore utility which takes incremental snapshots of the system using rsync and hard-links. These snapshots can be restored at a later date to undo all changes that were made to the system after the snapshot was taken. Snapshots can be taken manually or at regular intervals using scheduled jobs.

This utility is designed to protect only system files and settings.

If your looking for a tool instead to make a snapshot of your user files, I would suggest taking a look at some of these alternatives: rsnapshot, Back In Time and TimeVault.