When in Junktown, talk to Thomas, the power plant technician. He will ask you to inspect the malfunctioning Mr Handy that you will find standing around inside the power house.
During the inspection, you will probably obtain a random low-tier item.
After reporting your findings to Thomas, you will be asked to go to the general store in the Hub to purchase a functional robot motivator for Mr Handy. The part will cost you 800 caps unless your charisma and/or speech are high enough, in which case you might be able to negotiate a much better price.
Optionally, if you wish not to spend any money at all, you can salvage the motivator from one of the robobrains that can be found at Sierra Army Depot rather than buy it.
Having acquired the motivator, go back to Junktown and install the part in the robot. After successful installation, you will be rewarded with 500 experience points.
Note: Install the part in the robot by talking to it and choose option to replace part with new one.
Talk to Thomas again to successfully finish the quest and get another 500 experience points as well as a set of Super Sledge blueprints.