I am new to blender animation and there’s a problem saving the file. When I save it into my file the next time I opens it it changed to a new blender page with the unanimated cube. Is the saving process any different from the others? Thanks 
No, there’s no difference if your scene contains an animation or not. The keyframes are saved into your file automatically.
As a reminder, the basis of animation in Blender: In Object mode, select your object. Insert a keyframe. [I] --> Location. Move a certain number of frames forwards on the Timeline. Move your object. Insert an other keyframe.
Go back to the beginning. [SHIFT Left_arrow] Play! [ALT A]
[ESC] to stop.
Now you save and when you re-load, [ALT A] will re-play the animation. If it doesn’t… you have a problem. 