What do pilots do on a windshear alert after V1?
V1 is the calculated decision point at which takeoff must continue. Unless the aircraft is suffering a catastrophic failure, the pilot should not abort takeoff after V1.

The danger when taking off during windshear is the sudden lost of airspeed may result in the airplane settling back on the ground after it has become airborne. The technique, therefore, is aimed at gaining ground clearance in the shortest amount of time possible. In general, this involves:


Apply max thrust
Delay rotation
Once rotation is initiated, quickly pitch up to gain altitude


Below is an extract from the Boeing 777 FCOM about taking off when windshear is suspected (my emphasis):


  
  Takeoff with less than full rated thrust is not recommended (...)
  Use the longest suitable runway (...)
  Consider increasing Vr speed to the performance limited gross weight rotation speed. (...) If windshear is encountered at or beyond
  the actual gross weight Vr, do not attempt to accelerate to the
  increased Vr, but rotate without hesitation.
  (...) Minimize reductions from the initial climb pitch attitude until terrain and obstruction clearance is assured, unless stick
  shaker activates.
  (...) Stick shaker must be respected at all times.