Before you can put new strings on your bass guitar, you need to remove the old ones. You should always replace all your bass guitar's strings at the same time because they all wear at about the same rate. Replacing them all simultaneously ensures that they all sound the same.
The quickest way to remove your old bass strings is to simply take wire cutters (sturdy ones; bass strings are pretty thick) and cut the string at the thin section between the tuning post and the nut. Be sure to keep track of which string is connected to which tuning post. After cutting the string, simply pull the coiled end of the string off the tuning post, and then pull the other part through the bridge.
If you’re not careful, the string could whip back toward your face when you cut it. You can prevent this by turning the tuning head to loosen the string's tension before you cut it.
If you want to save your strings as a spare set (in case one of the new strings breaks), release the tension until you can grab the coiled end and pull it off the tuning post. Straighten the end of the string as best you can, and then pull the entire length through the bridge.
Take all your bass guitar's strings off before putting on the new strings. Your bass can handle it, and it gives you access to your fingerboard and pickups for some basic cleaning.