Translation:I am reading a book.
First!, Sorry for my English haha second this form is called T- Form and have some rules, for example, you must to take the form masu and change it, the verbs ending in U or group 1, change like this: the verbs ending in い、ち、り you must take out masu and add って。for example かいます change to かって、まちますーまって、かえりますーかえって。the verbs ending in に、み、and び、add んで、for example よみますーよんで、あそびますーあそんで。The verbs ending in き、add いて、かきますーかいて。verbs ending in ぎ、add いで、およぎますーおよいで。verbs ending in し only add て like this して，けしますーけして。There are exceptions like いきますーいって。
In group 2 or verbs ending in る、is easier, only take out masu and add て、for example みますーみて、ねますーねて、たべますーたべて、おきますーおきて。 And the last group 3 or irregulars ia like english, there are not especific rules , but is the same for example しますーして、べんきょうしますーべんきょうして、さんぽしますーさんぽして、きますーきて、かいものしますーかいものして etc. These is all, again sorry for my english, i still studying and i hope you can understand this form, because is very important in japanese. :-)
Why is it "I'm reading a books" instead of "I read a book"? What gives away the present continuous form?
In which context would you say this instead of "I read a book" or "I read books"?
"I am reading a book" expresses present transitive. It differes slightly from "i read a book" in that with the -ing ending we express that the activity is happening right now while the other form isnt specific to a certain time. From this i assume the japanese is expressing the present transitive?
This sentence does not imply who exactly is reading the book. Therefore, I think that “You are reading a book” and similar answers should be accepted.