I recently published a new book of translations from old/middle Irish into English and as sometimes happens when the subject comes up people are asking me how I learned the language and for suggestions on where to start themselves. For those who aren't aware old and middle Irish are the predecessors of modern Irish, in much the same way that old and middle English are the predecessors of modern English, and even if you speak modern Irish you would have to learn old and middle Irish separately.
Learning old Irish, as with any language, is best done from teachers who are fluent in the language themselves, however that isn't always an option. I am entirely self taught because there wasn't any way for me to attend classes on the subject. And I will warn people learning a language, especially one like Sean agus Méan-Gheailge, is difficult and requires dedication and a degree of stubbornness, as well as a willingness to hunt for any and all helpful materials.
Below I am going to give a list of both free online resources as well as books (not free) that a person could use to learn this language if they wanted to. These are the ones I have personal experience with and recommend but are not the only things out there.
Free Online Resources:
Memrise, a good way to learn vocabulary https://app.memrise.com/course/1155705/sengoidelc-old-irish-for-beginners/1/
Through the University of Texas Linguistic Research Center https://lrc.la.utexas.edu/eieol/iriol
Old Irish conjugated prepositions on Quizlet https://web.archive.org/web/20210212034949/https://quizlet.com/10767887/old-irish-conjugated-prepositions-flash-cards/
Pronunciation guide https://www3.smo.uhi.ac.uk/sengoidelc/donncha/labhairt.html
the electronic dictionary of the Irish language aka eDIL, a dictionary of old and middle Irish http://www.dil.ie/search
UCC's online Irish Texts, a source for the original material with parallel English and modern Irish translations http://iso.ucc.ie/index.html
Books available to purchase:
Old Irish Verbs and Vocabulary by Anthony Green
Sengoidelc: Old Irish for Beginners by David Stifler
Old-Irish Paradigms & Selections from the Old-Irish Glosses with notes and vocabulry by John Strachan
Old-Irish Workbook by EG Quin
Dictionary of the Irish Language: Based Mainly on Old and Middle Irish Materials by EG Quin
Old Irish Reader by Rudolf Thurneysen
A Concise Old Irish Grammar and Reader by Julius Pokorny
A Student's Companion to Old Irish Grammar by Ranke de Vries
An Introduction to Old Irish by RPM and WP Lehmann