In most cases you can send or receive free text messages from your email like you would any other email. It is free for you at least, although the receiver may pay to receive it depending on their text message plan.
To send a text message to a friend using your regular email account, you address it with the 10 digit phone number @ the email Web site URL of your friend's cell phone carrier. Note that's not the same as their main URL, it's a special one for text messaging. For example, AT&T is email@example.com, Verizon is firstname.lastname@example.org and T-Mobile is email@example.com. For other carriers, search "how to email text message to cell phone" on the support section of their Web site to find the text message email address.
Anyone can send you a text message from their cell phone to your email by entering your email address in the "To" field.