Initially, this new string may have trouble staying in tune. You can help correct this problem by stretching out the new string. Grab the string, and pull it approximately one inch away from the surface of the guitar. The pitch of the string will probably have dropped. Re-tune the string, then repeat the process, until the string no longer falls out of tune.
Once you've completed changing the sixth string, repeat the process for each additional string on your electric guitar. Changing strings is a process that is challenging and time consuming at first, but after you've done it a few times, becomes a simple bit of regular necessary maintenance.
Good luck!