From a terminal with the appropriate permissions enter
Now comment out, remove the #, one of the mirror selections; it would be best to pick from that is close to you. Once done press the control key along with X at the same time and save the file.
Before using for the first time you will need to update the GPG key. You do this from a term by entering
slackpkg update gpg
You will only have to do this once.
Now you are ready to run updates. The commands to enter one at a time, in the order that they should be entered, as each finish are: