Ancestry.com has a help article with details, however it doesn't cover how to get a shareable link without actually emailing it to someone or posting it on Facebook or Twitter, and doesn't detail how to save the image of the record from the sharing link, so that's what I'm going to cover.
|Click the "Share" button and select an option
For Ancestry.com subscribers:
1. Open any record on Ancestry.com that you want to share. Maybe you want to share it on Facebook or other social media, or you're adding it as a source to a collaborative tree like FamilySearch or Wikitree.
2. In the upper right area, click the "Share" button (shown above) - if the Share button doesn't appear, try refreshing the page. There will be three options, one to email someone a link, one for posting it to Facebook, and one for posting it to Twitter. If you're actually doing one of these things, then just select the appropriate option. Be aware that when selecting Facebook, it does not seem to give you the option to post it to one of your Facebook groups, let alone a specific topic within a group. So this is only an option if you want to share it in your newsfeed with all your friends. If you do want to post it in a specific topic in a Facebook group, use the following option instead...
|To get a shareable link to copy and paste anywhere, close the popup window
3. To get just a shareable link that you can copy and paste to anywhere, select either the Facebook or Twitter option (the email option doesn't work with this for some reason) but instead of posting it to Facebook or Twitter, close the popup window. Either click the little X in the upper right corner of the popup window, or click "cancel" (shown above). The window will close and then a new popup window will come up with the option to copy a shareable link (shown below). Click the URL once and it should select the link, then right click it and choose "copy". You can then paste it anywhere you want.
|Copy the sharing link to paste it anywhere
For non-Ancestry.com users:
1. Whenever you see an Ancestry.com link to a record that includes the word "sharing" in the URL, that means it's a shareable link and you'll be able to view it even if you don't have an Ancestry.com account or subscription.
|As you can see, the transcription of the record is limited in the shareable view
2. When viewing the record, if it includes an image you want to save, first click on the image or the "click to zoom" option that comes up over it when you hover over it (shown above).
3. A popup window with the full image will appear - you can zoom in to read it better, but it does not matter what the zoom setting is at to save the image. There's no Ancestry.com option to save the image so you have to use your browser's option. Right click the image and select "save image as" or "save picture as" or whatever similar terminology the browser you're using says (shown below). Then name and save the image to your computer as you normally would - make sure you note where you saved it so you don't have trouble finding it later.
|Save the image to your computer
Hope this helps, have fun sharing!