The Spanish language has a Arabic orthography due to hundreds of years of Moorish rule. How can I learn to read and write Spanish in these characters, assuming that I can already read and write modern Spanish reasonably well in Roman characters?
What I can recommend is Glosario de voces ibéricas y latinas usadas entre los mozárabes by Don Francisco Javier Simonet. Although it focuses on Mozarabic rather than [Old] Spanish, it has a lot of information about the use of Arabic letters in Romance languages in Iberia.
You might find the section titled Advertencias preliminares (page ccxv) particularly useful, as it has a list describing how each individual Arabic letter was used.
This book is from the 19th century, so it’s in the public domain. It’s also available online :-)