Not Financial Advice:
In order to trade stocks using E*Trade you'll need to open an account with them.
The web site will walk you through a series of questions to determine which type of account you wish to open (e.g. U.S. vs. Non-U.S., Individual vs. Joint, etc), who you are, how you'd like to fund your account, etc.
Once your account becomes active, trading stocks is simply a matter of entering the ticker symbol, and choosing some options.
For example, if you wished to purchase some shares in Apple, you would place your order by entering Apple's ticker symbol (AAPL), how many shares you wish to purchase (the number of shares times the current price per share would need to be equal to, or less than the purchasing balance your account has), preview your order and, if it's exactly what you want, authorize the web site to execute your trade (in this case a BUY order).