How can I best go about learning Hebrew?
The best way to learn is by immersion in the language. Yet, not everyone can surround themselves with Hebrew speakers. If the main reason for your desire to know Hebrew is for study, make sure to read, read, and read. If its the Hebrew of the Torah you want to learn, I recommend taking one chapter of the Torah and reading it in your native language and then rereading it in Hebrew. Do so even though you're not sure what the Hebrew says, or feel you understand nothing of what's written. Be patient. This will change with time. As you begin noticing certain Hebrew words repeating themselves, take note of those words and write down their meanings on the page.
Once you feel fairly confident in your understanding of the Hebrew of that chapter, move on to another chapter. Return every now and then to the chapters you already mastered to refresh your memory and ensure you will not forget the words you already learned. ' Do the same thing with the Mishna or whatever other text or type of Hebrew you want to learn.
If you're wanting to learn Hebrew to aid in Torah study, I'd say you should give the Written Torah priority. If you are able, read through the weekly Torah portion twice in Hebrew every week. Each weekly Torah portion is divided into 7 sections called aliyoth. You can use these 7 aliyoth as a means for easing the burden of reading the Torah portion twice a week in Hebrew by reading just one of the 7 aliyoth twice each day. By reading each of the 7 aliyoth twice a day, you will have completed the Torah portion twice by weeks end, without even realizing it.
Again, don't try to understand every word while familiarizing yourself with the text. Just read through the text, allowing your tongue and mouth to get used to forming the words. Allow your ear to recognize common words, even though you may not yet know the meaning of those words.
Once you definitely recognize certain words to the point that you're noticing them relatively frequently, it means that these words are already implanted in your memory. It's just a matter of plugging their definitions in place. If you stick with it, you'll be understanding the majority of the Hebrew text of the Written Torah after just one or two years, and with little effort. Consistency is key! I think it is much easier to learn Hebrew in the above manner rather than through forced memorization of long word lists.
Unless the person has amazing self control and super motivation, I think that most people are more likely to succeed in learning Hebrew by taking it slowly, not force feeding themselves vocabulary. Rather, by slowly building up their vocabulary though constant and consistent familiarization with the language, they will be less likely to burn themselves out. Aquiring vocabulary through constant reading also gives one the satisfaction of progress. In memorizing words directly from word lists, one only learns the individual words in that list. Building vocabularly through familiarization with significant passages, on the other hand, enables one to memorize the text, despite not understanding its content, in addition to the benefit of building vocabularly and giving the satisfaction of making headway in the text at hand.
REMEMBER: When reading a text, sound out the words as loudly as you're comfortable to sound them out. This will aid you in recognizing and memorizing words far more than if you read in a whisper.