I'm aware that there are very few ways to make fries that are not vegan, or at least vegetarian, but there is an art to making really good french fries from scratch. 
It seems pretty simple, but the easy way out makes good fries.  The more complicated way make amazing fries. 
You start with potatoes.  Clean them.  Peel them if you want, or leave the skin on if that's what you want.  Cut them into fries.  Keeping them kind of thick makes for a nice texture or soft potato inside a crunchy exterior. 
The complicated way: 
Put the sliced fries into a large bowl and cover them with cold water.  Leave them in the fridge for at least an hour, up to 12 hours.
After the soaking, drain the fries and pat them dry with a clean cloth or paper towels.
Heat up some vegetable or peanut oil in a heavy pot (dutch ovens work best, or any heavy bottomed pot) over a med-high heat. 
Heat small batches of fries for about five minutes.  This is step one, so the fries will not be heated all the way, just drain them and set them aside. 
After they are all heated the first time, raise the temp of the oil to high.
Put the fries back in the fryer for 5-10 minutes until the outsides are golden brown. 
Drain on paper towels and add salt and pepper to taste.  A coarse sea-salt is always my favorite for fries.
The easy way:
Skip the soaking and the first round of cooking.  Just cook each batch until they are golden brown on the outside and enjoy. 
The more complicated way will give you a better flavor and texture to the fries, but the easy method will also deliver fries that are way better than the bags you buy in your freezer section.