What would be the easiest/quickest way to get somebody who isn't computer-literate set up to have the ability to transfer money to me via Bitcoin? Also, Bitcoin touts that it is anonymous. Is it any more anonymous or untraceable than a simple cash transaction?
The easiest way would be to create an online wallet on blockchain.info, and use one of the easy deposit features it offers. This however is impractical both for traceability (his, not yours), and for fees (which might even be higher than the taxes AFAIK).
That said, bear in mind that usually you might convince people to use bitcoins when they have something to gain, not when you do: consider carefully why should they do it before asking them to.
LocalBitcoins.com offers secure and easy ways buying bitcoins locally in-person. There traders are very friendly towards novice bitcoin users and LocalBitcoins.com has messaging system where the buyer can ask about the bitcoin and get help how to set it up and.
Go to LocalBitcoins.com and enter where you are into the location search box
You'll see a list of nearby traders who are selling bitcoins to you
LocalBitcoins.com is in-person and you are discussing with a local trader, so language should not be a problem
Buy bitcoins with cash or online banking. Note that buying bitcoins is always safe, since LocalBitcoins.com has public reputation history of traders and holds bitcoins in escrow process until the trade has been succesfully complete
After bitcoins have been bought they appear in LocalBitcons.com website wallet
From there the person can directly transfer bitcoins to you
In the United States, by far the easiest way to get up and running is with Coinbase. It's very easy to get up and running - anyone who has a bank account can buy bitcoins with Coinbase by providing them with a bank account number and routing number. Aside from being a Coinbase customer, I'm not affiliated with them.
Since this is how I bought my own bitcoin stash in the past, here's what you need to do to buy bitcoins on Coinbase:
1) Register an account on Coinbase.com.
2) Provide your bank account number and routing number and wait a few days for them to send you a small amount of money to your account so they can verify that you actually control it.
3) Confirm the transactions they sent. 4) Decide how many bitcoins you want to buy, and initiate the transaction from Coinbase.com.
That's it. The bitcoins will arrive in the account about five business days later, if my transaction with Coinbase is typical.
I have to address what you said about Bitcoin being anonymous, however. Bitcoin is not anonymous, it is far less anonymous than cash in that all transactions are stored forever in the blockchain. In that sense, it is far less anonymous than cash since with bitcoin, if someone knows your bitcoin address, they can track what you spent your bitcoins on, what the recipient spent your bitcoins on, and so on. Unless you use a mixer, bitcoins are definitely not anonymous.