Javascript can`t save data on server. JS can save data on clients machine. Data on clients machine can be stored using cookie. But I feel, it isnt an aim. Store data from froms can server side apps, driven like php.

You can use filesaver.js library for a clean implementation or follow along with this codepen It is the quickest.

if you wanted to store input values assign all values in an object then JSON.stringify then throw it to this function to get text file of json

function createTextFile(str){
    var file = new Blob([str])
        anchor = document.createElement("a")
    anchor.href = URL.createObjectURL(file)
    anchor.download = "fileName"
    anchor.click()
    URL.revokeObjectURL(anchor.href)
    anchor.remove()    
}

var input = "this is a string to test"
createTextFile(input)

and if you wanted to save in server side with php there is function in php file-put-contents