If you want to tighten your cable, (to pull the mech closer to the wheel) you wind the adjuster OUT at the shifter, as you wind the thread out on the adjuster, it makes the outer cable longer. This effectively makes the inner cable shorter, pulling the mech.
For an example, shift the mech to the middle of the cassette. Gently but firmly pull the outer cable away from the shifter, as the cable outer moves away from the shifter, the mech will move towards the wheel.
Turn the adjuster just a half turn at a time, after each adjustment, shift through the entire range of the cassette. (make sure the chain is on the middle chainring at the front) No point getting it perfect for the low gears, and then finding you can't get the high gears.
Sometimes the adjusters have little notches to stop them turning by themselves, so just pull them out whilst turning. But as long as it turns, it doesn't matter if you pull them at the same time, or not.