What connections do I make to this Through hole DC Power connector
Centre pin is, well, the centre pin. Usually this is the positive supply voltage, but sometimes it's earth (ground, 0 V) - you need to check the details of the supply you're going to plug in to it.

Sleeve connects to the other contact on the plug - usually earth (ground, 0 V) but sometimes positive supply.

Sleeve shunt is probably a spring-loaded contact which connects to the sleeve pin when there is no plug inserted, but is open circuit when a plug is present - this can be used to disconnect an internal power source, for example. Test your connector with a resistance meter though, to check how it actually behaves.