Bad news: you can't get your start menu back without downloading third party software. You can, however, hit the "Windows" button at the bottom of the keyboard. Think of it as your new start menu button. Press the "Windows" key and begin to type the program you want (for instance, "Wordpad" or "Microsoft Excel". You should see an "Apps" screen:
When you see the application you are looking for, click on it with your mouse.
Helpful tip: if you'd rather just see all of your apps at once, press "Windows" + "Z" when you are at the start screen. Hit return to see "All Apps" and a screen with all of your applications should appear.
Do you only have a few applications that you use regularly (Firefox, Microsoft Word, Google Drive)? There's an easier way!
When you are on the larger apps screen, right click the application you'd like to pin to the taskbar. Then use your arrow keys to move to the left and choose "Pin to Taskbar" and hit Enter. It should look like this:
All "checked" applications will now appear on your taskbar when you hit "Windows" "Z"
Helpful tip: if you "pin" the Desktop to the start menu, you will be able to go straight to it from your Start Screen. Then, all of the items you have pinned to the taskbar will be along the bottom of the screen.
Please note: when you are on the "Desktop," there is still NO start menu! You may see some of the programs like the old, conventional desktop, but your choices are limited. Either press the Windows key on your keyboard or hover over the bottom left side of the screen to access your program lists.
If you ever get stuck you can always hit either the "Windows" key on your keyboard or hover over the bottom right of the screen. Options will show up on the right side of the screen, including both a return to the Start Screen and a Search option.
HOW TO TURN OFF COMPUTER: "Power" can be found under the "Settings" button when you hover over the bottom right side of the screen. This is where volume, wifi, and brightness settings are as well.
Here is where most of the pictures in this page were taken from, it goes into a bit more detail about navigating without a start menu: http://www.techrepublic.com/blog/window-on-windows/you-dont-really-need-a-start-menu-in-windows-8/6954
There are also video tutorials from Microsoft: http://windows.microsoft.com/en-us/windows-8/tutorial (However, most of this site is geared toward a touch-screen, so make sure to read the instructions above about navigating Windows 8)