Use File → Save or the F S keyboard shortcut to save your modified schematic page. Do it frequently to not lose your design. Unsaved pages are marked with an asterisk before their names in window titles and with little ‘Save’ buttons on tabs they are open in.
Use File → Save As... or the F A if you want to save your file under another name. In such a case, the Save As dialog box will be opened prompting you to input the file name you want. The same dialog will be opened automatically if you save a newly added and not yet saved untitled page. See Save As dialog box.
Like in the File Open dialog, you can use the filter entry below and choose the file type you need: schematics, symbols, schematic and symbols, or any files. Two first options change the saved file extension as well.