Replace one string at a time to keep the neck under tension.
Use the tuner to loosen the old string until it is visibly loose. I use a needle nose pliers to pull the end from the tuner. Then remove the loop end from the tail piece.
Connect the loop end of the new string to the tail piece. Thread the new string trough the tuner hole. Holding the end with my fingers, I turn the tuner until the string starts to grip. I turn the tuner until the sting gets close to in tune, then I stretch the sting by pulling with my fingers and then I tune it again. Repeat the procedure for all the strings. You'll have to retune constantly for the first ten minutes but about in a half hour things should be a lot better. I still am amazed how good an instrument sounds with a new set of strings.
If you decide the change strings a lot. Buy yourself a winder, it makes the process go much faster.