Web-based email (also called webmail) services like Gmail, Windows Live Hotmail and Yahoo Mail are free and you can access them from any computer and even your mobile phone. When using these services, there are many security considerations. First, you want to protect your account from being accessed by someone other than you. Use a strong password - it should also not be words found in a dictionary, but rather a mix of at least eight letters and numbers, changing cases and using symbols ($!* etc.) if allowed. To know more about password security, see also "How do I choose a good password?"
Next, look at your "security questions." These are the questions that will recover your password if you should lose it. The answers to these questions should not be ones that can be guessed easily. If you are given the option to write your own security questions, do so, and make them as obscure as possilble. Even lie in the answers if you feel it will make it harder to guess. This will secure your account from anyone else retrieving your password.
Finally, always remember to log out when you are finished using your webmail account. This is especially critical if you are using a public computer, as not taking this step can leave you logged in and at the risk of strangers viewing your private email.