There is not a lot to the flight director.
On the attitude indicator, you get two yellow markers (on the 510ED it's two orange lines - one vertical, one horizontal)

It simply gives a visual display of what the autopilot says you should be doing.
So, say you want some guidance down the ILS, but don't want the autopilot to actually fly the aircraft. You would tune your NAV1 radio to the ILS, select GS AUTO on the A/P, but not engage the A/P.
Then you fly to match the yellow markers, trying to keep them at the end of your 'wing tips' in the attitude display (orange triangle).
If the yellow markers move down, you lower the nose. If they rotate left, you go left etc.
So long as the yellow markers are on the end of your wings, you are on the correct attitude according to the autopilot.
Difficult to explain really.
I never rely on it myself & am not convinced it always works properly.
DM