How do I wire for an automatic battery backup??? Answered

I am working on a project where components are run from AC power (converted to 12v DC). I am interested in wiring in a 12V li-ion battery that will be trickle charged by the AC power (actually the converted 12v DC) and will automatically take over should the AC power go out.

To all you electronic geniuses -- how do I accomplish this likely easy setup.

Thanks in advance for the assistance.