The Chicago Manual of Style, section 14.253, (linked below) provides explanation and examples on how to reference plays, including Shakespeare. The pinpoint at the end of the footnote can/should include act, scene, and line number, e.g. 1.1.15-20 and the first time you provide these details add the phrase, References are to act, scene, and line (see King Lear example via link below). Subsequent, short form footnotes can omit the author's name if it's clear from the text (see more on this via the short forms link below).
Other important details to include are the editor and publication details. If you are using a play from an online source, such as Drama Online, you will also need to include a DOI or URL.
Example: Play (text) from Drama Online
First footnote
William Shakespeare, The Tempest, ed. Alden T. Vaughan and Virginia Mason Vaughan (London: Bloomsbury, 2011), 1.1.20-26. References are to act, scene, and line. https://doi.org/10.5040/9781408160183.00000045.
Subsequent footnote
The Tempest, 1.1.28-32.
Bibliography
Shakespeare, William. The Tempest. Edited by Alden T. Vaughan and Virginia Mason Vaughan. Arden Shakespeare, 3rd ser. London: Bloomsbury, 2011. https://doi.org/10.5040/9781408160183.00000045.
