Before you begin taking strings off your bass, have a good look at how the current ones are placed. The strings should be coming off the groves in the nut at the neck of your guitar. They will either pass or bypass holders and will either be going clockwise or counter clockwise around the tuners. It is essential to remember whether they bypass the holders and which direction they are wrapped around the tuner as you will have to replicate the same direction.
Next, you must loosen the first string, using the tuner, until you notice that the wraps on the winder have loosened, considerably. Once the string has loosened, pull it away from the tuner. There will be a little bend in the string from where it was stuck into the tuner. Now turn to the bridge of your guitar and pull the string out from that end. If it is difficult to grasp the end of the string at the bridge, you may have to push the string through and then pull.
You now have an opportunity to clean your bass guitar, under the area where the strings used to lie, do so with a soft cloth. Note how long your old string was and cut your new one to the same length.
Pull the new string through the same gauge in your bridge that you removed the previous one from. Thread the string around any guides, in the same manner that the old one was placed. Pull the string tightly if you want tension and wrap it around the tuner. You should have at least two wraps, but no layer should be overlapping. Stick the extra string back in to the tuner, securing it in place.
Hold the end of the tuner and turn the key so that the string becomes tight, do some rough tuning at this stage.
Carry out the same process for the other strings and do a final tune up when finished.