Thanks to Google Scholar, you can follow citations of an article you are the author. Is there any way to that for an article you are not the author?
Search for the paper on google scholar in the "Search" field.
In the search results, it will say "Cited by" below each hit, and if you click you can see the citations.
Moreover, once you see the list of citations, there is an option "Create alert" on the left which allows to create an alert alerting you when the paper is cited.
Whlie user151413's response is correct regarding Google Scholar, one could add some other possibilities (as your question seemed open-ended), such as the following:
Altmetric / Dimensions
Find the relevant Altmetric page of the publication and click on "Alert me about new mentions", which includes scholarly citations as tracked through Dimensions. See this screenshot:
Find the relevant publication and click on "Alert", as in this screnshot:
Go to the relevant publication and click on "Follow"; this is, as far as I know, not an e-mail alert, but it allows you to track the newest developments regarding that publication through your profile menu. The "Follow"-button looks like this:
Web of Science
Open the details page about the given publication and click on "Create a citation alert" on the right-hand side: