I use Sharebuilder for buying and selling stock. Since I'm still only starting out, I don't have a lot in there (no more than a couple thousand), and my purchases have never been for more than a couple hundred dollars at a time. I've always been curious how stock sales and purchases are handled with much higher volumes. Can the well-known groups of online trading sites handle trades in the hundreds of thousands of dollars? How about millions? Is there some kind of special process that needs to be gone through for larger purchases, or does it not really make a difference?
Do you mean kinda big amounts, or REALLY big amounts (like Warren Buffett-sized amounts)?
Stocks on the American markets are traded in lots of 100 shares (called "round lots"). For these amounts you can either call up a broker or go to an online brokerage and place your order in directly to the floor. It's executed in seconds (usually) and you have your shares for a commission of a few bucks.
This is in contrast to what you're doing with Sharebuilder. You can buy in less than 100-share increments, but you're paying more per share in the long run to do so because you're actually buying an allocation of a round lot from Sharebuilder.
If you're buying a whole lot of shares, then usually you have to do so gradually (and not tell anyone you're doing so, especially if you're Warren Buffett). If you were to put an order for 1,000,000 shares at once, you could end up paying a lot more than you need to because it might not be the case that there are enough sellers to sell you 1,000,000 shares at near the current price. The price will go up until your order is filled, but that could take a while.
Trades of very large amounts of stock are called "block trades." They are usually handled by a large investment house (typically NOT a Charles Schwab or TD Ameritrade).
The logical buyer for "institutional" amounts of stock are other institutions. A Goldman Sachs (or Morgan Stanley) will call up Fidelity, T. Rowe Price, Vanguard, etc. and say, "an institution has so many shares they want to buy (or sell) around the market price. Do you have a bid (to buy) or ask (to sell). The brokerage house will then go back to the first institution with a price. If there is a "match," the deal is done. In large size, this is called a "cross." Kudos to the broker.
Usually it's around the "old" market price. But because of the large size, it might not be. If it's off, it might set a "new" market price.
Some brokers offer special order types for handling this. For example, Interactive Brokers has a "Accumulate / Distribute Algorithm."
Accumulate/Distribute is a sophisticated trading algorithm which allows one to buy or sell large orders by splitting the trade into multiple orders with the goal of reducing visibility and market impact.