I think this question is asked quite a few times in forums everywhere, and it was until recently that I had the same question myself. On my way to Google, I was having a bit of a brain fart trying to remember how to change it. For the longest time I put "Change logo details" on my mental to-do checklist. I would type my website and all my old info would show up. I am in my first year (10 months today) and I am consistently learning and researching new ways to make YOU, my clients very happy!! SO anyways, "How do I get my Facebook preview to look right??" Perhaps you are here today because you have started a new Squarespace account, or like me...you started to re-brand and a few things have changed?! You want all your current info to show up. I get it...it makes sense! I would too!
STEP 1: Fill in the appropriate sections on your site
Make sure you've got an image and description text all set up on your website. On Squarespace sites, Facebook and other social media sites will pull the image and description text from a set list of fields: usually the Social Sharing Logo, but for specific pages (like blog posts, products, or events) from that page's thumbnail image.
So it's very important that you upload a Social Sharing Logo! Head over to Design > Logo & Title from your menu, and scroll down to the Social Sharing Logo section. Upload the image that you would like to have as the default image shared when you post your link on Facebook (note: the current recommendation is for this image to be sized at 200x200px).
While you're in this section, go ahead and fill out the Site Title / Tagline section at the top, if you haven't already. The site title is a key place to add keywords for SEO purposes, and the tagline is shown in Google search snippets as well. Then scroll up and click SAVE.
STEP 2: Debug and refresh your Facebook preview
Facebook has provided a very nifty debugger tool, which can do all kinds of in-depth things. You do not need to be a developer or have any coding knowledge whatsoever to make it work for you for these limited purposes!
Head over to https://developers.facebook.com/tools/debug/ and enter your URL in the box provided. You'll have to do this for every new page or post you create, so remember to enter the specific URL for the page in question, not just your top-level website address. Then click Debug.
The next screen will have a whole host of information on what Facebook sees when you post that URL. It's all relevant to this question, but none of it needs to be understood at this point. Simply click "Scrape Again" (in some older versions of this debugger, it's "Fetch New Scrape Information") to make Facebook refresh the preview it has for your URL.
WAAAAH LAAAA! You should be good to go! Your updated image and text should now be seen in the Link Preview section of the screen.
Sometimes there are errors that result from any number of possible issues. The debugger tool will list those errors for you, and often doing a quick Google search of the errors listed will help you figure out how to fix them. This worked for me and now when I tag my website, all my info is up to date and more professional. More more info or answers, visit Facebook's Squarespace forum page Squarespace Photographers