Finding a function from a big amount of values

Question

I have a big amount off y values. Example (1,65,4,98,543,543,678,4,2,7...). The x values would be (1,2,3,4,5...)I know that there is an infinite amount of functions fitting the points, but I only need one off them. Is there a method to find a function fitting all off the points? I need to be able to do it by myself and not to use a a program or app, because I need to know how it works.