Er...
You can adjust stem height, for which you need whatever tool that's required to loosen the screw that's on top of the stem, in line with the fork.
Might be a hexagonal bolt, but is probably an Allen key. Undo a couple of turns, knock bolt down, pull/push on stem. When happy, crank down on bolt again. Don't exceed the minimum insertion mark if you want to go higher.
Then you can adjust headset preload, for which you usually need two wrenches. A specially slim one for the headset cup, and then you can use an adjustable one for the locknut above.
Can't determine what you mean by headset height.