I have a S&W 4006, great pistol, slight problem.

How does one go about adjusting the trigger?

With the slide off, the trigger will cycle the hammer in both SA and DA mode.  But with the slide on, the trigger won't cycle the hammer.  The trigger reaches the end of it's pull and looks to almost cycle but won't.  Any guesses as to what needs to be adjusted.

The single action also feels much longer than it used to (still won't cycle with slide on).

Any help would be greatly appreciated.

Sounds like a problem with the firing pin block (in the slide). I have seen several 9mm S&Ws with the tip of the activation lever (in the frame) broken off, which I think could cause what you are seeing. There might also be some trash or metal shavings, etc. inside the channel, which could limit the travel of the block. Compare the lever to another that you know is working and see if it looks OK...if so, my guess is this problem is within your slide somewhere...just a guess.

If it has the mag safety (if it was made without one, it will be so marked) the trigger should simply "freewheel" with the slide on unless you insert a magazine. I have seen a few cases of improper interface between the mag safety lever and a specific magazine or two, but this does not sound like your problem.

Good Luck