Enable the neck pickup if using an electronic tuner. Use a pick, not your finger. Tune the thicker strings first because they pull more on the neck of the guitar, effecting the tension on the other strings the most. Always start low and tune up (toward higher pitches), not down. Re-check until all strings are in tune.
Once the guitar is tuned for all open strings, check each string at the 12th fret (the halfway point). If its sharp at the 12th, then lengthen the string by tightening the screw at the bridge, thus moving the center point of the string closer to
the bridge. If its flat at the 12th, then shorten the string by loosening the screw at the bridge, thus moving the center point of the string closer to the the
nut. Now compare again with harmonics on the 12th fret. Every string should be perfectly in tune when played in all three ways (0, 12, <12>). If you want to be excessive you can check tune at the six frets that have all natural notes (0, 5, 10, 12, 22).
"Action" is the distance between the string and the fret board. Generally you want the strings as close to the fret board as possible without buzzing. Buzz is most likely to occur on the lower frets where the angle of the string is low. If you do change the action be sure to adjust the height of your pickups to the gap recommended by the manufacturer. This can have a significant impact on your tone.
When restringing a guitar leave the D & G strings in place until the new strings are installed and tuned, then replace the D & G strings. This maintains some consistent tension on the neck of the guitar. Be sure to wind the strings in the correct direction around the post to ensure they fall into the right slot on the nut. After putting the string through the post hole, allow enough string to wind around the post by pulling the string back two frets from the nut for the high e, and 1.5 frets back for the Low E. Then bend the end of the string at a right angle around the post, clockwise, and loop it under the inbound part of the string, as shown below.
Not covered here are neck adjustments. See your owners manual or guitar shop for more information on neck.