Installing the thing
Browse to extension manager in the administrator area of your website, and choose upload to install the plugin.
Navigate to the plugin manager and search for 'textcaptcha'. The plugin should appear. Click to load the options of the configuration.
Set the plugin to enable and then enter in your Textcaptcha API key which you can optain from http://textcaptcha.com/register
Once the plugin has been enabled and configured with an API key, you will have to tell Joomla to use the 'textcaptcha' on your registration form.
Navigate to user manager, and click on Options.
The options menu will appear for user registration, for the Captcha option choose "Textcaptcha for Joomla". If the option for it doesn't appear in your list then you may still not have the plugin enabled on your website. Go back to the plugin manager and make sure that the plugin has been enabled.