CAPTCHAs (Completely Automated Public Turing tests to tell Computers and Humans Apart) come from the English word "capture", created in 2000 by Luis von Ahn, Manuel Blum, Nicholas J. Hopper (Carnegie Mellon University), and John Langford (International Business Machines Corporation). Captcha itself is a form of challenge-response test that is used in computers to ensure the answers given are not the results of a computer or bot.
Tutorial
1. Login Forum
First, before you access the link to get the captcha link, you will need to login first as usual. If you keep trying it without logging in first, only errors will occur, like the picture below.
2. Get the Captcha Code
Next, just click this link (https://bitcointalk.org/captcha_code.php) to get the captcha link for the code that will be used to log in later. After getting the captcha link for the code, don't forget to save / bookmark it in a place that you think is safe.
3. Logout and log in again
Next, you try logging out and try logging in again using the captcha link code that you got earlier.
Good luck and hopefully useful