John Hobbins over at Ancient Hebrew Poetry has some good tips about learning Classical Hebrew.  John sets the bar high with his introductory paragraph:

If you want to learn ancient Hebrew so as to savor its sounds, understand the nuances of its words and expressions, and recognize the formal structures of its poetry and prose, then you will seek to make the language your own. A standard test of linguistic competence is the ability to engage in simultaneous translation from one language to the other, unaided by a dictionary. When you are able to translate ancient Hebrew into your mother tongue without the aid of a dictionary, you will have moved in the right direction. When you are able to translate from your mother tongue into ancient Hebrew without the help of a dictionary, you will have attained a degree of active competence in the language. Your sense of accomplishment will be great, and rightly so.

Do take a look at his suggestions, especially the resources he mentions that will allow you to make progress on your own.