Hi, I'm also new. I'll share my experience thus far and maybe it can help.
First: Download the Bitshares wallet from the website to your local machine and set up your username and password. Then export you wallet file to your computer, and save it elsewhere. (Flash drive, email, cloud, etc.) Now that the "keys" (the backup file and your password) to your personal "vault" (desktop wallet) are secure, you then need to register the name with the blockchain and then fund your account. Go to
http://faucet.bitshares.org to register you username. Once your username is registered with the blockchain, you can fund the account with Bitshares. But to do that, right now, you need to buy Bitcoin. In most cases, you'll buy a fraction of a single Bitcoin (In the beginning I assumed I needed to buy a whole coin, but this is unnecessary).
Next: The easiest way to get Bitcoin, for me (and in the same day and without much hassle) was to go to
Localbitcoins.com and create an account (an online bitcoin wallet essentially). You can search for various methods of deposit, but I searched for a cash deposit option with a bank in my area. The details of the account and the transaction are understood when you use the site and find a seller. Essentially you deposit cash and verfiy it with a receipt and then the seller sends your equivalent amount in Bitcoin to your Localbitcoins.com online wallet. You now have Bitcoin and can exchange it for other altcoins. Almost there.
Finally: Localbitcoins.com is a good temporary wallet, but you'll want to download another Bitcoin wallet for more security (Bitcoin Core, Electrum, etc). But if
speed is your main concern, then simply use your Localbitcoins.com wallet to hold your Bitcoins temporarily before exchanging them for Bitshares. This is where
Shapeshift.io comes in, as it is the most convenient exchange service available right now, by far. Your personal Bitshares username or public key is the receiving address. Shapeshift.io even has a live chat function if you need some extra explanation. By the time you're finished with the Shapeshift transaction (a few minutes), you should have Bitshares transferred to your local wallet. (sigh of relief)
As for what to do with your BTS once they are in your Bitshares wallet, this is becoming better explained with each new update. You can simply hold BTS or exchange them for BitUSD or some other asset. Or you can transfer BTS to another exchange, like
BTER.com. But I suspect the wallet will become more intuitive and more user-friendly as time goes on. One note about the Memo field. Usually when you
Transfer BTS to another wallet, the Memo field would be used to ensure the funds are attributed to the right account, and this information is usually provided by the receiving party. They will offer a reference number or something for you to include in the Memo field. In the case of BTER.com for example, when you want to deposit BTS to an online BTER account, they will provide the Memo details.
Good luck!