Talk to Ingram after completing Spoils of War to start this quest. Head to the airport and plug in the Berylium Agitator on Liberty Prime. Now go back down and activate the Power transfer switch to initialize Prime. Now follow him as he makes his way to The Institute. There might be spots where Prime just stops moving due clipping so make sure to save often. Synths will teleport along the way. There's also a portion where Prime will cross the river. Go on ahead and eliminate more hostiles along the way.
Once you've reached the CIT Ruins successfully, you'll find more BoS forces engaging the synths. Take them out and defend Prime as he tries to scan the ruins. More synths will teleport in so make sure to kill them as fast as you can.
Once Prime successfully breaches the ground, jump through the hole to enter The Institute to complete the quest. If you have “Form Ranks” active, it will be completed at the same time as well.