Bitstamp are big in Europe and, since 2011, have moved from Slovenia, and the United Kingdom in search of sound regulatory environments. Good volumes are available for larger trades. Well received by people using SEPA and credit cards. Both euro and US dollar deposits are accepted. I like Bitstamp because they really focus on being a pure bitcoin-only exchange (update: since 2017 Bitstamp have started adding popular cryptocoins). Please read my Bitstamp critique for analysis of factors such as security, fees, and the history.
With a Google Doc, all parties have access to the same document at the same time, and the most up-to-date version of that document is always visible and editable to all parties. This real-time shared Google Doc is just like a distributed blockchain ledger. The “real version” of the transaction is verified by analyzing all the available blocks on multiple computers and taking “the average”.
Ethereum is an open-sourced, public blockchain-based platform that enables the development of decentralized applications along with smart contracts. Ethereum focuses on running the code of these applications rather than being a peer to peer electronic cash system like many other cryptocurrencies. The project enjoys enormous community support and boasts the most significant active developer community in the cryptocurrency space. Scalability on the network is an issue, but there are many projects underway to address these issues.
Once you are ready to place an order, you will accept the market price or set what’s called a limit order. Limit orders provide investors and traders with a means of precisely entering a position without being victim of fluctuating prices. For example, a buy limit order can be place for $2.40 when a stock is trading around $2.50. If the price dips to $2.40, the order is automatically executed. If it’s a GTC (good ’til canceled) order, it will remain open until manually cancelled by the investor.
Bitcoin was developed through technology that executes completely online. It is stored virtually, on wallets or exchanges. Everything is online and one can remotely transfer and send value to anyone online (stored in bitcoin as a currency). One can’t touch their bitcoins the same way one can touch physical things such as a dollar bill, computer desk, a tree etc.

In March 2017, various blockchain start-ups, research groups, and Fortune 500 companies announced the creation of the Enterprise Ethereum Alliance (EEA) with 30 founding members.[23] By May, the nonprofit organization had 116 enterprise members—including ConsenSys, CME Group, Cornell University's research group, Toyota Research Institute, Samsung SDS, Microsoft, Intel, J. P. Morgan, Cooley LLP, Merck KGaA, DTCC, Deloitte, Accenture, Banco Santander, BNY Mellon, ING, and National Bank of Canada.[24][25][26] By July 2017, there were over 150 members in the alliance, including recent additions MasterCard, Cisco Systems, Sberbank and Scotiabank.[27][28]
The good news: No advanced math or computation is involved. You may have heard that miners are solving difficult mathematical problems--that's not true at all. What they're actually doing is trying to be the first miner to come up with a 64-digit hexadecimal number (a "hash")  that is less than or equal to the target hash. It's basically guess work.

It is possible that the Ethereum Platform will not be used by a large number of external businesses, individuals, and other organizations and that there will be limited public interest in the creation and development of distributed applications. Such a lack of interest could impact the development of the Ethereum Platform and potential uses of ETH. It cannot predict the success of its own development efforts or the efforts of other third parties.