I think you are describing a pump jack that has been placed over a well which has a sucker rod..several sections... and moves up and down to bring water to the surface.
I've pulled the sucker rods on wells that still had the metal structure over them... you pull the rod up and typically have to unscrew several sections until you get to the working parts at the end. The actual pump sits in the water and that's where the leathers are, at the very bottom of the well.
Yes, you MUST be careful to not drop the whole thing down... if you do, it's a delightful fishing expidition.. expensive in time and money.
Assuming a tower over the well, you rig a rope pulley and pull the whole thing up. I had specially made wrenches which would fit on the sucker rod metal fittings and function both as a wrench and device preventing the sucker rod from dropping back into the well. Unscrew sections as necessary utill you get to the bottom section where they actual pump device is. At this point, everything is out of the hole.
Sucker rods are typically made either of wood or fiberglass and 20 feet long. You have to consider the total weight of the entire rod... obviously heavier when you start and gets lighter after you remove some sections.
Shallow wells of maybe three sections you can pull manually ,,, but stuff is slick and you have to be very careful to attach stuff so it will not slip from your grip.
It's been a long time. I did it by myself when in high school in 1960. The end of the pump where the leathers are must have been rather easy to figure out because I recall thinking that I it was easier than I had anticipated. My well was 320 feet.
Reading your post... since it would be only $100 for someone to come out and do it.... your well must be very shallow and easy to get to. If you are at all mechanically capable, I would not be afraid to do it myself. Best idea would be to bribe a buddy to come give a hand....
I googled for the topic and suggest you look at these sites.. they may also be helpful.
Water Well Helpline
Lifewater Drilling & Well Construction Manual: Table of Contents
Cylinder cup leathers for use in piston type well cylinders for pumping water. has all sorts of leathers
DEAN BENNETT SUPPLY at 800-621-4291 is your water well pump and windmill supply store. he has parts for all windmills
Good luck!
