Wax the new bowstring and check it for any flaws. Waxing the string will make it easier to install and extend the string's life. Set the waxed string aside.
Set the crossbow into the bow press. Use a bow press that is approved by your crossbow's manufacturer. Slowly compress the crossbow limbs to loosen the string. Using a bow press reduces the possibility of the string breaking while you're changing strings.
Install the new string over the old string while it is still on the crossbow. Follow the old string, placing the new one over the old one. Carefully remove the old string without dislodging the new string.
Inspect the crossbow while still in the bow press. Check the limbs, pulleys, cams, stringer and stock and ensure that all parts are in proper working condition.
Release the bow press tension and remove the bow. Check the crossbow's alignment to make sure it did not get bent while in the press.
Test out the restrung crossbow at an archery range. Cock the crossbow checking that the cams roll freely and the string does not bind. Fire the crossbow to check that it works properly and shoots straight.