You can unlock this sidequest by talking to Purah after you have completed the main quest “Locked Mementos”. Learn more about it here.
You will need to travel to the northern area of the Akkala Region. Here you can forge Ancient Armor, Ancient weapons, and Ancient Arrows, which all can provide you an easy way to kill Guardians. To get to Akkala and the Akkala Tower you can go north from Ploymous Mountain, which is near the Zora’s Domain.
Follow the footpath that passes the South Akkala Stable and you will find the lab standing alone in a forest. On the way to the lab is a stationary Guardian that is awake so watch out for it.
When you enter Robbie’s lab, speak with the weird robot-like device in the center of the room. Once Robbie has expressed his suspicions, strip off all your armor and equipment to confirm that it is you.
Now, just like when you first met Purah at Hateno Village, you will need to bring a blue flame from the nearby local furnace and light Robbie’s furnace to kickstart the lab. You can easily Paraglide to the furnace but bringing the flame back will involve walking around the hills and getting past a lot of enemies. Kill as many as you can on the way there, and then on the way back here is an easy method you can use.
First, get the blue flame to a nearby torch. Light it. Defeat the enemies nearby however you wish to. Then return to the torch, light your own torch, and proceed to the next torch. Repeat until you have made it back to the lab.
Now the modified Guardian Stone inside Robbie’s lab will allow you to exchange Ancient materials and Rupees to craft Ancient weapons and gear. If you haven’t tried to infiltrate Hyrule Castle and defeat Ganon, Ancient Arrows are extremely useful at defeating Guardians easily and quickly, so maybe make a few of them.
At this point the sidequest is complete. For those interested in 100%ing the game, be sure to craft the weapons for your Hyrule Compedium and buy the Guardian armor set!