Note: this guide is horribly out of date at this point, so take everything with a grain of salt. I am leaving this article here as it is for posterity.
My best friend +Ian Decker recently got the HTC Thunderbolt, and it is his first Android phone ever. So I figured I should be a good friend and influence the way he uses his phone. Note: most of the links in this article go to the Google Play site for that app, where you can conveniently click "install" and that app will install on the device you selected. No need to even touch the device.
Step 1: Picking your device
Android devices run the whole spectrum of price, size, and even shape. Everyone has their preferences, but the one thing that I can say to everyone is this: make sure that the device you are buying runs Android 4.0 or higher. There are a lot of apps that aren't available on older versions, and 4.0 is the cutoff for a lot of them. I also prefer stock Android to pretty much any skin, so I would recommend a Nexus or the Google Play edition of one of the third-party phones.
+Marques Brownlee has a great YouTube channel where he does reviews of tons of phones, so check him out.
Ian's reasoning behind getting the Tunderbolt was that it is the cheapest phone running Ice Cream Sandwich on the Verizon network. And being that it was the first Verizon phone with 4G/LTE I'm sure it is a quality phone, if a bit dated.
Step 2: Apps
It's important to find quality apps for all of the things you will be doing with your device. Google makes really good first-party apps, but sometimes there are third-party alternatives that are better.
Most of Google's apps come pre-installed, but if they aren't you'll have to go grab them.
Chrome: I know that there are a lot of browsers on Android, and some of them run more smoothly than Chrome; however, I've stuck with it because it syncs with the desktop version of Chrome.
Gmail: by far the best email app out there.
Maps: this ain't no Apple Maps. It's never steered me wrong, and Google's collection of Street View images is unbeatable.
Search: the Google Search app is so much more than just search. Google Now strives to give you the information you need at any given time, before you have to ask for it. The weather is always there for your location, and things like your next appointment, upcoming flights, tracking packages that are being shipped to you, updates on sports, nearby events, and time to get home are displayed when appropriate. It is the most useful feature of having a device that is always with you.
Calendar: how else will you keep track of your life?
Google Drive: it is surprising how many different types of documents you can edit with the Drive app.
Keyboard: Google's stock keyboard for Android 4.0+ just blew the competition away with gesture typing and voice dictation all in one keyboard, and now even people with non-stock devices can use this wonderful app.
Goggles: this is a pretty cool app that will search by taking a picture. If you see a painting or landmark that you don't recognize, try taking a picture of it with Goggles. It also recognizes QR codes.
My Tracks: I used this app to record some hiking trips we went on during our trip to Yellowstone.
Cloud Print: Google originally came up with this when they invented ChromeOS. If you need to print something but you're using a device that isn't connected to a printer, send it to cloud print and your computer at home will print it for you.
Keep: great for quickly jotting things down for later. It can also store pictures and voice recordings as notes.
Google Music: definitely the easiest way to get your library onto your Android device. Install the Music Manager onto your computer and upload your music files to Google. You can then play them from any computer or Android device. Their new All Access program is a great deal: everything in their store for $10 a month. I don't think that I will ever buy music again.
Google Books, Kindle, Nook: no matter who you buy books from, there's a way to read them on Android.
BeyondPod: I know you are all faithful listeners of my podcast and many other podcasts. BeyondPod is my favorite podcast manager for Android.
Feedly: this is definitely the best alternative to the late Google Reader (may it rest in peace.) If you don't use an RSS reader, you should really start. It's incredibly useful for keeping up with comics, blogs, and news sites that have new content on a regular basis.
Hangouts: Google's integration of their chat services is complete, and Hangouts is the result.
Google Voice: even if you don't have a phone, you can still have a phone number! Google Voice allows you to text and make calls over wifi, and it synchronizes with the desktop version.
Skype: not as good as Hangouts, but maybe you have friends who are only on Skype.
Google+: my favorite social network.
Facebook: not the best designed app, but it sure beats using their mobile site.
I'm sure that whatever social network you enjoy using has an app. I know for a fact that there a bajillion Twitter apps.
I haven't been gaming a ton on my Nexus 7, but here are a few suggestions.
Superbrothers Sword & Sworcery: if you like story-based games, music, and/or tongue-in-cheek humor, you will love this game. I know I did.
Super Hexagon: This is a really fast-paced reflex game where you just try to last as long as possible without getting hit by the edges coming towards the middle of the screen.
Beat Hazard: an Asteroid-like twin stick shooter where the pace of the enemies and the strength of your weapons is determined by the music you are playing. It's a blast.
Keep an eye on the Humble Bundle. They occasionally have Android games.
There are emulators available on Android, but I haven't checked any of them out. I believe that the legal stance on emulators is that if you own the game itself, it is legal to have a ROM of that game.
DashClock: I like this widget because it displays a lot of important information at once. The time, unread email, upcoming events on my calendar, etc.
ES File Explorer: one of the things that Android lacks is a proper file explorer. This is usually fine, but power users will definitely want to install this one.
Steam: PC gamers will want to get this app so they can access the Steam chat, store, and community pages.
Wifi Analyzer: I don't know what half the things are that it tells you, but there it is.
Voice Recorder: a nice simple audio recorder.
Zombies, Run!: this is the best motivation for running that I have found. It narrates a story for you while you run, and anytime there are zombies nearby you have to run faster.
MTG Counter: if you play Magic the Gathering you've probably gotten tired of having to keep track of how much life you have left. This app does that and has a dice roller.
Adblock Plus: I've never met anyone who has said that they like seeing advertisements on websites. It will also sometimes prevent ads from popping up in other apps, which is probably why they aren't in the Play Store anymore.
Step 3: Customization
Now it is time to make your device your own. Organize your apps. Change your wallpaper. Put some widgets on your homepage. Change your ringtone. Android is endlessly customizable. This is really a matter of personal preference.
Step 4: Enjoy!
Go to town and start using your new Android device. And let me know if you find new stuff that I don't know about.