How can I setup a LED state change with push buttons?
This is an excellent tutorial for exactly that:
http://www.instructables.com/id/How-to-use-a-Push-Button-Arduino-Tutorial/

Its a bit hard to give you a specific answer without seeing you circuit. 
but as a start, i would set the ledPin to LOW in the setup routine. 

void setup() 
{ 
  pinMode(ledpin,OUTPUT);
  pinMode(pushbutton1,INPUT);
  pinMode(pushbutton2,INPUT);

  //initialize the pin to low
  digitalWrite(ledpin,LOW);

}