If you google something like "position interpolation" you might get better results. Interpolation is just the transitioning from one state to another state through some middle states. For you, this means transitioning from one position to another position through the positions between them.
Think about it this way: if you want your movement from Point A to Point B to take 10 seconds, after 5 seconds you want your object to be halfway between Point A and Point B (assuming linear speed). The algorithm looks something like this:
//called before movement starts
Position startPosition = currentPosition;
Position endPosition = whatever you want;
long startTime = System.currentTimeMillis();
long duration = 10*1000; //10 seconds
//called several times a second
update(){
long elapsed = System.currentTimeMillis - startTime;
newPosition = startPosition + (endPosition-startPosition) * (elapsed/duration);
}