I'm-a try to summarize it as best as I can with my limited knowledge:
For each one of these types of coins (bitcoins, litecoins, dogecoins, etc.), you basically download a free program for that coin, called a "wallet". Open the wallet on your computer for the first time, and you'll have to wait a few hours to let it sync. Once that finishes syncing, you're ready to receive (and later send) coins on your computer.
You receive coins by giving someone your generated address that leads to your wallet (it'll be a long string of letters, like DbGdXfRGRvGeVFefEFsceGFEe). You can have multiple addresses to receive coins with.
You send coins by simply specifying the amount you're sending, and sending it to the person's address (which they'll give you)
MAKE SURE to encrypt your wallet.dat file (don't EVER delete this as long as you have coins on it), and make sure to use a secret, unique passphrase for your wallet so nobody can steal your shyt. Also make sure to make copies of your wallet and put it on separate USB sticks, to be safe. Try not to use any "online" wallets, either (check out the Christmas dogecoin hack for why)
How to get coins?
If they're one of the cheap-ass ones like dogecoin, you can actually beg for it on certain sites and people will actually just give it to you (some will give 10, 50, or 100....a few might even give 1000 depending on how much they have). Or you can visit a "faucet" site (basically a site that gives like 1-10 cheap coins at a time for free to any user who simply puts in their wallet address). Don't look to do this shyt with the more valuable coins like bitcoin/litecoin
More than likely, you'll be buying coins direct, though. There are forums specific to each type of coin where you can trade with other users (be careful with forums though.....nikkas LOVE to try to scam you on there. Always use a trusted, mod/site-approved escrow when buying/selling. fukk a good feedback/high rating, that don't mean shyt. I seen nikkas got scammed by well-established forum members. This shyt ain't no joke. You can also try using paypal while buying/selling but most people don't fukk with that, since the buyer might send the money, get the coins then do a chargeback and claim they didn't get the coins.....and they'll get their money back, leaving the other person screwed)
You can also trade on reddit (with escrow). Or you can use one of the various exchange sites to safely buy and sell coins.
You can also "mine" the coins. I don't know too much about that shyt, but it seems like you basically leave your computer running and you have to leave some program running so it actually produces the coins. Apparently you need some good computer hardware to do this as well. I don't fukk with that mining shyt since I ain't no techie-type, and plus that's money wasted with electricity so you're technically paying for it, anyway
Now.....why spend money to buy fake-ass internet coins in the first place?
And this is where the gambling aspect of it comes in. You're basically investing. You're hoping for the coins to increase in value after you buy them, so you can sell them and make a profit later (like I did

). Some people are even hoping that some of these coins will eventually shoot up to a crazy value like bitcoin did. You gotta follow the forum talks (especially the bitcointalk forum) to see which coins are a waste of time, and which ones actually have long-term potential, and are going somewhere.
With all that shyt said....I only fukks with bitcoin, litecoin, dogecoin (and another coin that I'm keeping to myself for personal reasons

)
GET SOME DOGECOIN, THOUGH......but wait until after it crashes, then hold onto it for like a year to see where it goes. Someone's manipulating the dogecoin market right now and pumping the fukk out of it (thanks to whoever that is

), so a major drop in value is expected soon, which will be the best time to buy