I think that the most effective approach to teaching article usage depends mainly on the specific teaching context involved, since in the ESL classroom we typically teach students of diverse backgrounds and native languages, whereas in the EFL classroom we almost always have the luxury of students with the same native language, but who usually have the disadvantage of much more restricted access to comprehensible and grammatical input. Assuming the typical ESL context, in this case, a mixed class of first language speakers including Arabic (with a frequently-used definite article but no indefinite article), Chinese, Japanese and Korean (with no articles of any kind), and Spanish (with both a definite and indefinite article which are used in ways that often do not overlap with their English counterparts, including the fact that both types of Spanish articles are inflected for number), I would still use contrastive analysis as a strategy for helping students learn how articles are used in English. I believe that it is critical for adult learners to understand the differences in how articles are used (or not used) in English and their native language in order to master this aspect of English grammar (the same could also be said for many other grammar points). Since L1 interference tends to be robust and persistent in article usage (as it is in the usage of prepositions), I believe that completely ignoring the linguistic particulars of each student's native language just because of the teaching context (i.e., a class consisting of students with different and diverse native languages) would not be an effective strategy. Allowing students to explore the differences in how English and their native language deal with articles (or in the case of some languages, avoids them entirely) may also help sensitize students to the manifold ways articles can be used in different languages, thereby raising their general linguistic awareness while at the same time validating the importance and legitimacy of their native language, which can often be an issue in the ESL context.
I recommend presenting each article (indefinite, definite and null/zero) in separate lessons, with the indefinite article coming first since Folse (2009) urges that we always teach English count nouns as "language chunks" with the indefinite article included given that in English, we almost never use the singular form of count nouns without a determiner. I would then present each separate use of the articles as a discrete lesson, addressing the most common uses first. I would make sure that throughout the lessons, sufficient attention is paid to helping students of each language address their L1-specific difficulties (e.g., overuse of the definite article by Arabic speakers, underuse or random use of articles by Chinese, Japanese and Korean speakers, and the specific incongruities between article usage in Spanish and English).