This is how I learned.
Step 1
Remove most of the old fishing line off of the spinning reel. Leave just enough line through the spool end of the rod to attach the new fishing line to.
Step 2
Make 2 clinch knots to attach the new line to the old.
Step 3
Lay the new spool of fishing line on the floor. Position it so that it comes off the new spool exactly as it will go on to the spinning reel.
Step 4
Secure the fishing line tightly with your free hand. Slowly turn the spinning reel with your other hand, making sure that the line winds on tightly.
Step 5
Fill the spool until it is about an eighth of an inch from the spool tip. This should only require about 50 yards of fishing line. Don't fill the entire spool, or you risk tangling the line.