A possible approach is: don't bother.
One philosophy of learning language is to get the grasp of general grammar and necessary vocabulary and work out the details later (I refer to this as a philosophy rather than an approach, because it is still too general.) That is, you learn what is absolutely necessary for communicating and being understood, hoping that you patch the wholes - like not using correct genders - later.
This is a practical approach for somebody who lives in a country and needs to master the language as quickly as possible in order to survive, find a job, communicate with the in-laws. This is not a good approach, if one aims at speaking beautifully and correctly, with a good accent, especially if the language is your professional tool (e.g., if you do research in linguistics, write books, or take interviews as a journalist.) In fact, the don't bother approach almost precludes you from ever learning to speak language correctly - surely with time you will memorize the gender of the common words and lots of shortcuts for recognizing the word gender, but incorrect use would by then fossilize and require constant conscious effort to keep in check. Still, I think it is worth mentioning.
Interlanguage fossilization is when people learning a second language keep taking rules from their native language and incorrectly applying them to the second language they are learning. This results in a language system that different from both the person's native language and second language.