You have the transformer wired already? If you did then..
With the relay socket positioned vertical.
Depending on the relay socket that you have. There should be corresponding #s assigned to each terminal/post.
Transformer and float are terminated to #7 & #8
If the socket terminal has no corresponding #'s. 7&8 are the terminal right blow the 2 parallel line. Float wire terminate on the left, transformer wire terminate on the left.
As for the power/extension cord. If you haven't done so.
Pick a wire (doesnt matter, which one) and separate from the other wire. Be careful and try to keep the insulation intact. Also, you are going to make this cut at a spot that will give you enough slack to reach the wall outlet.
The 2 cut end will terminate on #4 and #6.
Again, with the relay socket vertical. #4 and #6 will be top left post/terminal and bottom left post terminal.
This should trigger the relay to open when the float drop and provide a complete circuit to turn on the pump.
Something to consider...
You should implement a some form of a "siphon break" in the output from the rervoir. Test the setup for about a week, before applying to your system
What voltage is the coil? I would highly recommend using a 12V coil, you don’t want to apply 120V to the float, even if its rated for that I rather not have it that close to the water. You need to run a transformer in series with th coil and the float.
For the electrical, always interrupt (switch) the hot, never the nuteral. If your relay is DPDT you can do both but never just the nuteral.
You have to figure if your float is set to NO or NC most floats can be changed by removing the circlip and flipping the float mage net upside down. If your float is set to NO than you want to connect the hot wires to COM and NO, this is the way I would reccomend as the coil is only energized when the water level is down.
FWIW, I have one already wired just plug in wall, clip on floats and plug in the pump. PM me $20 shipped.