While a mouse certainly makes a quick and efficient job of navigating a Microsoft Excel 2013 spreadsheet, keyboard shortcuts can perform the same fundamental actions. Use Key Tips to switch tabs at the top of the screen. To switch between worksheet tabs along the bottom, use a "Control" combination shortcut.
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To switch tabs on the ribbon at the top of your spreadsheet, start by pressing the "Alt" key to invoke the app's Key Tips functionality. You'll notice that each tab on the ribbon is labeled with a letter -- for example, an "N" appears over the Insert tab and a "P" on the Page Layout tab. Press the letter key that corresponds with the tab you need and Microsoft switches to it.
The tabs along the bottom of the Excel window represent worksheets. Press the "Control-Page Down" keyboard shortcut to switch from sheet to sheet moving from left to right. Similarly, "Control-Page Up" moves through worksheet tabs in the opposite direction -- from right to left.