The easiest way to start would be introducing an invisible form field [0] and on submission, checking if it is not empty. Give this form field a random name so that it wouldn't be populated by password managers.
You can take it one step further and check how fast the form was submitted. If it is below the predefined threshold, it is probably a bot.
[0] To hide the form field, you can use one of these snippets, interchangeably:
"display:none;"
"position:absolute!important;top:-9999px;left:-9999px;"
"position:absolute!important;height:1px;width:1px;overflow:hidden;"