Step 1: Get yourself a wallet (app/client) such as Coinbase, Blockchain, Electrum (beginner's guide), Mycelium (Android), Bitcoin-Qt (now Bitcoin Core).
Step 2. Obtain some Bitcoin - Ideally someone will have given you some, or you can buy some from someone local. Another possibility is gifting yourself some with eGifter or other services.You can always convert dollars to bitcoin. You will need to provide your identity if you are going to transfer dollars into bitcoin with one of the wallet services (such as via ACH, wire or credit card).
Step 3. Advanced - Mixing Transactions. When you actually go to do transactions, you may wish to use a mixing service like Send Shared (SharedCoin) to mask the funds original source by mixing them with other funds. Services typically charge a 1% fee.
Step 4: Check out the local Bitcoin community and the increasing number of ways to spend and earn Bitcoin. OpenBazaar is a decentralized marketplace for instantly trading with anyone using Bitcoin - local anonymous trading - maybe supplanting or augmenting eBay and CraigsList. LocalBitCoins remains an expanding local resource for buying and selling Bitcoin, and there are of course Bitcoin ATMs and kiosks.
Where did Bitcoin come from?
The primordial Bitcoin or stone blockchain is Rai stones on the Island of Yap, used exactly as in the current purpose, as a public ledger of economic transactions inspectable by all.