To stabilise a wormhole, you must first scan it by entering the system with a Pathfinder class of ship. Then you must command a ship with the Integral Stabilisation perk and then orbit an unstable wormhole in a system your faction owns. Once in orbit, click into the body to view its details. Use the Stablise Destinations section and choose the stabilise option for the faction system you desire. You will then be able to choose any faction system to connect the wormhole too.