Reading the first post seems simple enough. Reading the second post just hurts my brain (maybe because it's 1:25AM).
Upon plugging a HDMI cable into the laptop/TV, the laptop should immediately register the external monitor. The default action taken depends on the facotry settings. Acer seem to like switching display to the external monitor whilst PB and HP seem to like duplicating the display across both screens. Dell, from what I've seen so far, like to ignore the external display until you tell it to use it. In any case, you should be able to either use a Fn key (like Fn + F5 - it's different with every laptop) to switch between display modes, or Right Click the Desktop and go to Properties/Display Settings/Screen Resolution (depending on your version of Windows).
You can set it to either use the external monitor alone, duplicate display onto the external (it'll be limited to the resolution of the primary monitor) or extend the desktop to the external. If you choose to extend it, you'll have to set the orientation of the two monitors (as in, are they side by side or is one above the other?) to allow your mouse to drag from one monitor to the other, and the resolution of the external monitor (which'll usually be much bigger than the primary monitor on a TV).
Sometimes laptop drivers get confused and switch the primary monitor to the external. It's difficult to change that back, but you can always make sure that it displays the task bar on the laptop monitor.