This short mission serves as an introduction to the duties of Spider-Man's alter-ego, Peter Parker.
After a bit of waiting around, you'll receive your next mission in the form of a call from someone labeled "Boss." Follow the waypoint to Octavius Industries to attend to this urgent matter. Press 
after approaching the door on the rooftop of this building and Spider-Man will become Peter Parker, lab coat and all. After the scene, you can examine some of the items lying around the lab for some commentary from Peter, including a recording left by Dr. Octavius about Peter. You can also listen in on the committee director's discussion with Dr. Octavius in his office, but to continue the story, follow the waypoint to the prosthetic arm.
Press to begin the test and 
to move the arm around. The arm doesn't seem to be working properly, so Peter must now attempt to fix it. Move over to the tablet to begin the diagnostics test, which will then lead into some mini-games. The first is a Circuit Project, which requires you to get the voltage to flow from the green octagon to the orange. The pieces on the board are locked, so you must simply fill out the empty spaces with connecting pieces in your inventory. Place a corner piece (you can use 
or 
while holding the piece to rotate it) on the spot where the voltage comes to a stop to keep it going, then place another corner piece above it. The next piece should form a straight line, and the spot to the right of the locked-in piece should be filled in by a corner. The remaining pieces should then be used to reach the finish. A full solution can be found to the right.
What follows the first Circuit Project is another Circuit Project, this one introducing circuit pieces that send the voltage in specific directions. You'll have to make a path to the right, through the locked-in piece to the left, and then back around to the right, which can be seen in the image to the left. The final Circuit Project requires you to incorporate some very basic math, as the pieces now increase and decrease the voltage by a certain number. By the time you reach the finish, you'll have to have a voltage totaling 3. This is made more complicated by the fact that addition and subtraction pieces must be placed over green and red outlines respectively, ensuring that there is only one possible solution. In this case, the solution is to insert a +2 piece, -1 piece, and another +2 piece, as can be seen in the image to the right.
The diagnostics test is now complete, meaning it's time to retest the prosthetic arm. Move it around with and notice its improved mobility. You can now complete more Circuit Projects at any time for additional XP and Research Tokens by accessing a tablet on a table in front of Dr. Octavius' office (though only the first two are available for now), but for this mission, you'll have to move onto another mini-game: Spectrographs. Follow the waypoint to a computer and press to begin.
Spectrographs require you to match the pattern shown using fragments in your inventory. Following the short tutorial, you should have an easy time figuring out the rest of the puzzle. Enjoy this simplicity for now, as these Spectrographs will only get tougher as the game goes on. Like Circuit Projects, clearing this puzzle opens up the opportunity to clear additional Spectrographs for XP and Research Tokens. You can press at this same station to get started on the first two, as all others are locked. To finish the story mission, simply exit the lab the same way you came in.