How does the pilot knows that the filght is airborne?

There is a very specific "rotation" speed that is reached, then back pressure is applied slowly so the aircraft lifts off. That speed is referred to as VR (velocity rotation) if you want the specific info.

VR rotation speed. The speed of an aircraft at which the pilot initiates rotation to obtain the scheduled takeoff performance. It must be greater or equal to the V1 speed.

Here is a list of V speeds http://aviationglossary.com/v-speeds/

Pilots learn these speeds for the aircraft they fly, it isn't random.

PS. It isn't the "vertical stabilizer" that tilts it it the elevator that is used. The vertical stabilizer or rudder keeps yaw under control and keeps the nose straight.

The pilot knows the plane is airborne by looking for a visual or instrument positive rate of climb--using the altimeter and vertical speed indicators.

The pilot 'tilts the nose up' or rotates at a certain speed, designated Vr. No planes use the vertical stabilizer to rotate, only the horizontal one and only if it is an all-flying tail on planes as diverse as the F-18 or Piper Cherokee. Most others use the elevators.

Okay, first off - the vertical stabilizer does NOT control pitch. The vertical stabilizer is there for directional stability, the rudder is mechanically attached to it and provides yaw control.

The horizontal stabilizer / tailplane provides pitch stability and only pivots for trim settings on most transport airplanes. The pitch is controlled by the elevator, mechanically attached to it. Tailplanes that move entirely to pitch the airplane up or down are called "stabilators" not elevators, and are commonly seen on modern high performance airplanes like the F-16, F-22, etc.

The pilots rotate the airplane at an airspeed called rotation speed or just "VR" for short.

And, um...well no offense meant, but you need to seriously work on your grammar: The title of your question is rather non-sensical. "Flight" and "airborne" are linguistically equivalent.

Hope that clears it up.

When the Airspeed Indicator is at the correct speed according to the aircraft type and weight. The aircraft can rotate (lift) if the air flow across the wings is fast enough. So lets say 130 knots was the rotation speed of the aircraft. If there was a 30 knot headwind, then the aircraft would still rotate at 130 knots. The only difference would be the ground speed. Speed in which the aircraft covers distance, not airflow. Watch a few take off videos on Youtube (inside cockpit) and you will hear the call outs. For example, the 80 knot cross check, the V1 call, Rotation call out. Then V2 when the aircraft is airborne. then the gear retract call. Very controlled and safe. V1 is the point of no return, meaning the airplane will not be able to safely stop should the pilot see a threat for safe operation.

When the flight attendant informs the pilot that the flight is airborne

Your question is, How does the pilot knows that the flight is airborne?

It stops vibrating.

Any other answer is from one whose never been at the yoke.

Heu... A proper rotation to get the aircraft airborne....