The term Yemeni Arabic actually comprises a bunch of different, really fascinating dialects. For example, the Zabidi dialect uses "am" for the definite article instead of the typical "al." It's generally difficult to find resources for Yemeni Arabic compared to more popular ones like Levantine and Egyptian. I personally found that Yemeni dialects are really difficult to understand, even if you know MSA and another dialect like Egyptian well.
Dictionaries
Deboo's English-German-Arabic lexicon is probably the most comprehensive, but lack examples and is all romanized. One of its best features is that is lists which region of Yemen words belong to.
Textbooks
By and large I've found most textbooks to not be of great quality for self-study. With a Yemeni tutor or teacher is probably the best way to go.
The
Adeni textbook focuses on the dialect of the city of Aden. In romanization.
Sbahtu! is a course in San'aani (the dialect of the capital city). No audio, all romanized.
The
Yemeni Institute for Arabic Language has produced a textbook series for Yemeni dialect, but they're not well suited to self-study. Basically, you need a teacher. Though I will say this is the first one that looks to me like a real full course in the everyday dialect.
DLI has produced audio lessons in a bunch of dialects including Yemeni. It includes lots of radio and media Arabic mixed with Fus7a. I don't think it's great for general learning, and clearly reflects the needs of the institution that produced it. It might be useful for some advanced learners.
Videos / Media / Music
A-WA is an Israeli-Yemenite trio of sisters who sing in Jewish Yemeni Arabic about the life of their great-grandmother in Yemen and her eventual migration to Israel. There music mixes modern hiphop with traditional Yemenite sounds. Although some have commented that their accents are non-native and maybe slightly off on a few words, the content and the grammar are authentic. I read that they collaborated with a professor specializing in Judeo-Arabic varieties.
Courses
YIAL apparently has online courses, though I haven't tried them.
Natakallam offfers Yemeni Arabic, with refugees and displaced people as teachers, tutors, and language partners. I highly recommend Natakallam.