I’m not at my gaming computer but I can try to do it from memory.
First, I’m using the Longitude Flight Dynamics improvement mod which improves the tune of the autothrottle.
Second, I don’t take off using autothrottle, but I know that others on the Longitude thread do. I have done it before but I like manual takeoffs better. They are more smooth to me.
I first push the TOGA button to set up the flight director. Make sure you have an altitude set. Then I take off using full power. Rotate and climb sharply to control airspeed. Stay below 250 knots. At about 1000 feet I throttle down to keep a reasonable airspeed (~220-250) and pitch around 15-20 degrees. Engage Autopilot to follow flight plan. Make sure the Speed outer knob is in manual. Turn it to 250 knots. Push my keybind for (Engage Autothrottle)?
( I forget the exact keybind name but I had two buttons bound for engage autothrottle and disengage autothrottle until I discovered that they seem to do the same thing. Now I use the same button for engage and disengage.)
Regardless, engage autothrottle and the aircraft should then moderately accelerate to 250 knots and pitch up to maintain it. Climb to preset altitude. Follow ATC or your own flight plan after that. Autothrottle should keep everything on track through cruise, descent and approach. On short final, keep your throttles low and disengage Autothrottle. Manually manage your speed until landing.
If you have further problems I suggest posting on the Longitude Flight Dynamics Improvement Mod thread where you can talk to the developer