Before starting to restring the blinds, examine them carefully, and figure out how the blinds work and why the string it attached the way it is. Try to remember how the blinds are arranged, or take pictures of all parts of the mechanism. This is going to help when you have to put the blinds back together.
To measure the size of the replacement string, wrap it around a pencil 10 times, measure the width of all the loops together, and divide that number by 10. Blind string sizes usually come in millimeters, so divide the size by 25.4 to convert it to millimeters. To find out how long the replacement string needs to be, measure the height of the blinds, the width from the furthest string and the hanging part of the string. Use the sum of these numbers.
Take the blinds off the window, remove all the parts that block the access to the top and bottom part of the blinds, and detach one string at either end of the blinds. Pull the new string through the base of the blinds and further through the row of holes. Generally, follow the path of the old string. You can use a tapestry needle or a loop of wire for this. Tie a knot at the bottom rail so that the string stays in place.
Reattach all the parts that you took off the blinds, hang them in the window, and check if they work properly.