Changing your strings is a very personal experience, and it varies. Our preferred way:
Change strings one at a time starting with your low E, unless conditioning your fretboard, or making other adjustments. (This is especially true with a Bigsby, or other floating trem system)
Remove the old string by detuning until completely floppy, cut in the middle by neck pickup. Pull through tuning peg and bridge. Make sure tuning peg is vertical relative to the fretboard, so a string will easily pass through flat.
Standard or locking tuners:
Unwind new string, and pull through bridge, and tuning peg until taught. Place your non tuning hand on the string just in front of the nut, and slide the string/your finger to the first fret. Keep your index finger in place, and begin to tune up, making sure the wrap goes under excess string, after the first revolution. This will help lock/hold down the string in place and prevent slippage. Tune to pitch. Cut off excess.
Vintage style Fender tuners, with open tops:
Unwind new string, string through bridge, and tuning peg until taught. With your non tuning hand, hold end of string taught through the peg. Grab cutting tool, and measure two tuning pegs away from where tuning peg is strung through and cut, leaving about 2” of slack. Place the end of the string in center hole in peg, and then crimp flat against base of tuning peg center. Tune to pitch, while holding index finger between nut and first fret. Make sure wrap goes over after the first revolution. This will help lock/hold down the string in place and prevent slippage.
Stretch your strings by grabbing the string with 8 fingers curled over, and thumbs gently pushing the opposite direction. Work your way up and down the length of the string, working them as you go. Tune them up to pitch, repeat this process until strings no longer drastically detune.
Repeat for other strings.
Note: smaller/higher strings will need less slack before you start your wrap.