Various models of sets have their own individual quirks.
I will really need the model number to be able to help you.
If you can not find your notes, the model number will be on a tag affixed to the front of the set.
You are correct in that this does not look complicated - because it is not.
This set has one of the most straight forward fuel pump changes there is.
The only warning on this one is do not lay directly under the pump when removing the fuel lines - there will be spillage.
Remove the fuel supply line from the filter and plug the line.
Loosen or remove the filter while the pump is still attached to the base (it just screws into the pump). If you are installing a new filter, disregard this step.
Disconnect the fuel line from the carburetor (you will have to cut the metal band). Note where the fuel line comes up through the base.
Disconnect the power wire to the fuel pump.
From under the set, remove the 2 bolts that hold the pump in, and pull the pump straight down.
Remove the fuel line from the pump.
Install the fuel line on the new pump. Make sure the protective wrap stays on.
Install the filter to the pump (you can tighten it now or after the pump is installed.
Installation is the reverse of removal.