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If this is your very first Android device, i would suggest, as Fred suggested, sign in to your gmail and set it up on your phone. even if it isn't your main email.
reasons for this are for one, you need it if you want to download apps from the play store. secondly, you can back up all your contacts to your Gmail and if you need to wipe your phone, all your contacts and app will all appear on your phone as soon as you sign into your gmail on the initial set up. (just make sure you connect to a wifi network, otherwise your apps will download over your 3G network and cry when your bill is printed)
Set up instant upload on your G+ account. think of it as a back up for your pictures. you have a private server all to yourself to store all your pictures. so again, if you wipe your phone, your SD card becomes defective, you have this back up.
Set up your Google Now account, and use google Chrome. i won't go into much detail for this one as it will guide you through it.
Other Apps I highly recommend are those that will enhance your phones performance. Now some of these are debatable by different users but for me, they are probably the best apps I have (also be wary of apps that drain your battery, I'll elaborate below):
1. Juice Defender: Great App that managers your data connection. When you lock your device, the data is turned off and when you unlock your device, you data reconnects. This is a great app to save you battery life when you aren't using your phone actively.
2. Smart Wifi Toggler: works hand-in-hand iwth Juice Defender because it toggles and memorizes your wifi connections. It will check periodically when you're not connected to data to get a wifi connection it know's of. With this, you will be able to not ever have to turn on and off your data or wifi. The phone apps will do it for you. (exceptions are private connections like a coffee shop because they require a sign in. Friends and family locations are fine so long as they never change their passwords).
3. Learn about NFC (Near Field Communication) and Android Beam. You can essentially LIFE HAX your everyday activites by buying these tags that your phone can scan, you can program what you want your phone to do, and just put your phone close to it to activate. For example, putting a tag in your car and programming it to turn off sound, turn on bluetooth. Put it on your dashboard and the second you get into the car, put it over it and it will do exactly that. No more fiddling with settings.
4. Last little thing to enjoy on your phone is to EXPLORE! You can customize the heck out of your phone with GO (and many other companies) that can change your skins, operating system look, and backgrounds.
I hope this helps. Let me know if you want to learn anything else about Androids.
On any smartphone nowadays, they have the capability to multitask. You can open more than 1 app at a time, but with that said, those apps are still "on." One suggestion to you is to hold down the "Home" button (main button of the phone) and close all your apps once in a while by tapping the button with an "X" on the bottom right side, or swiping away each app left or right.
Avoid Go like the plague, it is a memory hog and slows your phone to hell
recommended Launchers are Nova/Apex/ADW
if you want a different keyboard, swiftkey and swype are 2 very popular ones.
go on the play store and look them up