In the upper-left corner of the Blender window, select File and choose Save As from the drop-down menu. This opens File Browser, as shown in the following screenshot:

Click on the LMB where it says untitled.blend, as shown in the previous screenshot. The background behind the word untitled.blend becomes darker and you can edit the name now. When you have named the file, press Enter.

If you wish to increment the filename, that is, to have files named animation1.blend, animation2.blend, and so on, move the cursor over to the upper right corner of the window and click on the plus sign. Before you press the Save As Blender File button, make sure that you are in the right directory.

To go up a directory, click on the upward pointing bent arrow at the top of the list of files. To go into a directory, click on the icon that...