The actuating arm of the mechanical fuel pump is moved up and down by an "eccentric" mounted to the front of the camshaft timing gear. I suggest using a remote starter relay button to bump the engine over until the eccentric is at its lowest point, where the pressure on the fuel pump arm is at a minimum, otherwise you will be fighting the pressure of the actuating arm the entire time removing and installing the fuel pump.
There are a lot of YouTube videos showing how to replace a fuel pump. I even got in on that action, as I felt some of the videos were a bit terse or missed some steps I felt were needed. For instance, as recommended throughout this thread by several folks, you really want to remove the oil filter so you have room to work. But, there is another good reason to remove the oil filter. Often when the diaphragm inside the fuel pump fails, not only does the output volume and pressure drop or stop, with the actuating arm still going up and down, often liquid gasoline can end up leaking externally and/or internally. When it leaks internally raw gasoline gets inside the crankcase, which contaminates the engine oil, and keeps the oil from being able to properly protect the internally lubricated parts of the engine. You can pull the dipstick and see if the engine oil is higher than it normally is (due to fuel in the oil), or smells like is has gasoline in it. But, frankly, it is not worth taking a chance on the it having been contaminated or not. I suggest you just change the oil and filter out of an abundance of caution.
If you would like to look at the YouTube video Lynda and I put together you are welcome to. The links are provided below. In my case the engine is a 1973 302 in a 73 Mustang Convertible. If you are running a 351C the only significant difference is how the fuel pump mounting bolts are oriented (our bolts are on a horizontal mounting position, the 351C bolts are on a vertical mounting position). Also, When I thought the iPhone was in record mode during the installation of the pump it was not recording. So a bit of what normally would have been shown is absent. But, there is enough other information in the videos we did capture to be worth watching, iMHO.
Finally, while you are replacing the fuel pump it is a good idea to replace the rubber fuel lines at the fuel tank, the fuel pump, and even at the fuel filter at the carburetor. I show how to do that in the videos also.
Have fun! This is one of the easier repairs to perform.
Here are the YouTube links:
All inclusive video:
The following links are snippets of the video above, in case you prefer to look at it in its major parts.
Removing the fuel pump:
Preparing the new Fuel Pump for Replacement:
Replacng the rubber fuel lines at the fuel tank and at the fuel pump: