Help How to fully close an app?

Welcome here. Really you can just not worry about it. Android is most often best left running itself. Just use the back arrow button instead of jumping to your home button. Congrats on a very nice 1st ever Droid

You can use the home button too. Depends on if you want to go back or go home.

The important part is there's really no reason to worry about closing apps.

If you reaaaallllly want it gone (but you don't), you can open the task manager, and kill it there.

But you reaaaaallly don't ever have to do that. Ever.

Actually I did think of one case. If the app is a poorly written battery hog, you might want to kill it.
But for lets say normal apps, there's no reason to.

"Not worrying about it" is how you get terrible battery life.

There is a distinct difference between exiting an app with the home button and exiting an app with the back button.

If you exit an app using the home button, you're doing the equivalent of minimizing it in windows. It will still be using just about all of the juice it would be using if it was open full screen. Someone who makes a habit out of "exiting" all of their apps with the home button through the course of a day will end up with a dozen apps constantly using a bit of CPU time and as a result less than stellar performance and battery life.

Exiting an app with the back button is supposed(I say supposed to because a bad developer can neglect to put this behavior into the app even though it is supposed to be in all apps) to put apps into a sleep mode where they sit in RAM(so you could reopen the app very fast if you use it again) but do not consume any CPU or battery.

Exiting an app using the in app exit button should do the same thing as exiting it with the back button.

Where the wonky battery life issues on most Android phones come from is when a developer fails to have a proper sleep/idle mode for their app so it always consumes power just by being installed if you have ever opened it once since the phone has been on. There is no way to stop these apps from constantly using juice except with a task killer or force close. It is because of these apps that you need a task killer(assuming you absolutely must use a specific app and it does this). The ideal solution would be to just not use applications with this kind of behavior.