On a recurve bow it's very simple to replace the bow string, but this is what makes it safe. This is called a bow stringer. This is the way you should always replace or remove a bow string from a recurve bow. The cup goes on the bottom. The sling goes over the top. You put your foot on the bow stringer. You pull up, you remove the loop, and you let down. Therefore now the string has been loosened and can be removed. Very simply the string is off the bow.
In order to put the string back on the bow it's basically the same thing. You put your loop on the bottom, and you put the cup over it. You put the sling over the top and in front of the loop. You step on the stringer. You pull up, push the loop to the end, make sure it's secured, let down slowly, and the bow is strung.
The bow stringer has to be used with recurve bows. There is no other way safely to remove or to replace a bow string on a recurve.
On a compound bow it gets a little bit more complicated, because you need what we call a bow press. It's a device that is found in most pro shops. I would suggest that if you don't own a bow press that you bring it to a pro shop in order to get a string or a cable replaced or repaired.