If your site is in searchmysite.net, you can add a search box to your site with one line of code. See Website Search Tool for further details.
Note: To keep the public search free of spam, anonymous submissions are no longer allowed. If you have a personal website which isn't already listed, but don't want a Full listing or Free Trial, you can try requesting that a site owner with a Full listing (e.g. https://michael-lewis.com/) submit your site as a Basic listing.