Java: Optimize code

import java.awt.geom.*;

public class elevator

Class names are typically capitalized

{

    static int floor = 0, choice1, person = 0;

Prefer local variables to statics like this. Person doesn't appear to be used.

    public static void main(String args[])
    {

        floor = ((int) (Math.random() * 10 + 1));

You've got an extra pair of parens that you don't need.

        System.out.println("The elevator is now on floor " +floor);
        System.out.print("Which floor are you at now (0-10) where 0 = basement: ");
        choice1 = Keyboard.readInt();

        if(floor == choice1)
        {
            System.out.println("Enter the elevator");
        }

        else if(floor > choice1)
        {
            ElevatorDown();
        }

        else if(floor < choice1)
        {
            ElevatorUp();
        }

Rather then keeping your choice in a static variable. Pass it as a parameter to your ElevatorUp()/ElevatorDown() Movement functions.

        System.out.println("To which floor would you want to go (0-10) where 0 = basement");
        choice1 = Keyboard.readInt();

        if(floor > choice1)
        {
            ElevatorDown();
        }

        else if(floor < choice1)
        {
            ElevatorUp();
        }

This is repeated from before. Write an ElevatorMove() function that decides whether to call ElevatorUp or ElevatorDown.

    }

    public static void ElevatorUp()
    {
        System.out.println("The elevator is on it's way up...");

        for (person = choice1; choice1>=floor; floor++)

Declare for loop variables in the loop not some other random place. And person? What does person have to do with it? In fact person=choice1 does nothing. I'd make this a while loop.

            System.out.println(floor);

        System.out.println("The elevator has arrived");
    }

    public static void ElevatorDown()
    {
        System.out.println("The elevator is on it's way down...");
        for (person = choice1; choice1<=floor; floor--)

            System.out.println(floor);

        System.out.println("The elevator has arrived");
    }

These two functions are similiar. They can be combined. }

My reworking of your code:

import java.awt.geom.*;

public class elevator
{

    static int floor;

    public static void main(String args[])
    {

        floor = (int) (Math.random() * 10 + 1);

        System.out.println("The elevator is now on floor " +floor);
        System.out.print("Which floor are you at now (0-10) where 0 = basement: ");
        int current_floor = Keyboard.readInt();

        if(floor == current_floor)
        {
            System.out.println("Enter the elevator");
        }
        else
        {
            MoveElevator(current_floor);
        }


        System.out.println("To which floor would you want to go (0-10) where 0 = basement");
        int target_floor = Keyboard.readInt();

        MoveElevator(target_floor);
    }

    public static void MoveElevator(int target_floor)
    {
        int direction;
        if( target_floor > floor )
        {
            System.out.println("The elevator is on it's way up...");
            direction = 1;
        }else{
            System.out.println("The elevator is on it's way down...");
            direction = -1;
        }

        while(target_floor != floor)
        {
            floor += direction;
            System.out.println(floor);
        }

        System.out.println("The elevator has arrived");
    }
}

In object oriented programming, you typically ask yourself: which objects do I operate with, what can I do with them, and what are their properties? In your case:

• There is an elevator, and there could possibly be many elevators, which are all similar.
• An elevator always has a current floor where it currently is.
• That current floor can change when the elevator is in action.
• One typical action is to move up.
• Another typical action is to move down.
• When a person wants to use the elevator, the elevator moves to the floor where the person is. In general, the elevator moves to a certain floor.

And here is the code, based on the description above:

public class Elevator {

  private int currentFloor;

  public void run() {
    currentFloor = 1 + ((int) (Math.random() * 10));

    System.out.println("The elevator is now on floor " + currentFloor);
    System.out.print("Which floor are you at now (0-10) where 0 = basement: ");
    int personFloor = Keyboard.readInt();
    moveTo(personFloor);
    System.out.println("Enter the elevator");

    System.out.println("To which floor do you want to go (0-10) where 0 = basement");
    int destinationFloor = Keyboard.readInt();
    moveTo(destinationFloor);
    System.out.println("Leave the elevator");
  }

  private void moveTo(int destinationFloor) {
    if (destinationFloor == currentFloor) {
      /* nothing to do */
    } else if (destinationFloor > currentFloor) {
      moveUpTo(destinationFloor);
    } else {
      moveDownTo(destinationFloor);
    }
  }

  private void moveUpTo(int destinationFloor) {
    System.out.println("The elevator is on its way up ...");
    while (currentFloor < destinationFloor) {
      currentFloor++;
      System.out.println(currentFloor);
    }
    System.out.println("The elevator has arrived");
  }

  private void moveDownTo(int destinationFloor) {
    System.out.println("The elevator is on its way down ...");
    while (currentFloor > destinationFloor) {
      currentFloor--;
      System.out.println(currentFloor);
    }
    System.out.println("The elevator has arrived");
  }

  public static void main(String[] args) {
    new Elevator().run();
  }

}

By the way, the elevator is on its way, not on it's way.