Well, you can use a mop, a hockey stick, a shovel, or even a broom.
Ah sorry (doing day job stuff) You put the items in the blueprint slots. So click on the blueprint, then open the inventory and select the handle, and place it in the handle slot in the bottom right of the blueprint. Do the same for the coil in the coil slot at the bottom middle and finally the sensor in the first slot. (Once you know the correct sensor - it's named in the manual, which can be found in the first room on the floor. It'll be highlighted and say something like "[model numbers] Sensor Module")
Once you have placed all items in the blueprint, you can click "Build It" which is at the top of the screen (if you can't see it because of the inventory, just move your mouse down and wait for the inventory to close, then click the button).
there's a lamp hanging nearby which can reach it. but you need to make it heavier to successfully get the wire.
spoilers:
You will need the bucket, turn on the valve in the store room to make the pipe leak in the main room. Put bucket under pipe.
Get rope from bio lab.
Use rope on pipe in main room.
Get bucket, use bucket on lamp in bio lab.
Push bucket.