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Assuming you are using D8, here are some instructions (D7 would be similar but slightly different).
The metatag module has some submodules to help with various metatag usages. You will want to also enable the metatag_open_graph module. This will let you set the og* metatags.
First step in this is to go to the Content Type definition (structure->content types) for the page type (article?) you want to have metatag info on. You will need to select the Manage Fields option. Here you need to add a new field. Use the "Use an existing field" option and add the MetaTags field to the content type.
Repeat this for any other content types you want to have Metatag info added to.
Once you have done this, you can go into the configure / search and metadata / metatag screens and define the defaults you want either globally or for the specific content type. You can use "tokens" to indicate items from the node values. E.g. [current-page:title] or [node:field_featured_image] and the like. There is a browse available tokens to give you some guidance here.
Additionally, now that you have the metatag field added to the content type. You can also manually modify the metatags for any single node if you have the rights to modify the metatag info.
This can be done while editing the node and opening the MetaTag tab (generally at the bottom of the form).
To keep facebook and twitter happy I think you generally need the title metatag, og description field and the og image field set.