To take on a faction as advanced as The Institute, no time expense is too great, especially when it takes a dozen steps to build a giant robot. Your first step is to speak with and follow Proctor Ingram at Boston Airport. She will then tell you to bring on someone specialized in robotics to this project. If you successfully brought Doctor Li back to the Brotherhood of Steel in the From Within quest, the waypoint indicator will lead you to the good doctor. If you weren't successful, you'll be guided to another character, Professor Scara in the General Atomics Galleria. Either way, your subsequent conversations will result in the enlistment of a robotics expert.
The next step is a resource gathering objective that leads you to a randomly selected hospital. Whatever location you're given, you have to specifically find magnet parts, which are thankfully indicated on your Pip-Boy.
Return to Boston Airport and enter Workshop mode. You'll find the specific magnet build project under the Special category. You'll need to make four actuators. Once you have those made, you'll be ready for the next phase.
Now you'll be tasked with entering the atomic blast zone in the southwest corner of the map. Be sure to have a couple Radaways handy, or better yet, a power armor. Meet up with Scribe Haylen at Waypoint Echo near the edge of the Glowing Sea. The project demands a set of nuclear bomb packs, and while you're not tasked in retrieving such hazardous materials, you will be asked to tag these nukes with a distress pulser so Haylen's team can pick them up.
This will take you to Sentinel Site Prescott, a path that will lead you through highly irradiated areas. Once inside, progress downward through the maze-like gentry. You'll also need to terminate a blast sequence to open some blast doors. Wind your way through the tunnels, and you'll eventually reach Henri, one of the many Children of the Atom.
You being a stranger, Henri will be reluctant to hand over the atomic weapons to you. Rather than killing him (which is an option), you can convince him that you share a common faith and devotion to his nuclear god. Dead or not, the next step is to use Henri's password to open the doors leading to the bomb packs. Now that the nukes are tagged, take the nearby elevator to make a quick exit.
Return to Boston Airport where a very pleased Proctor Ingram will let you do the honors of activating a robot named Liberty Prime.