The best way to teach yourself ancient Greek is to purchase A Reading Course in Homeric Greek (Focus Publishing). If you already know Latin, then you will also want to buy Clyde Pharr's Homeric Greek. As you gain confidence, pick up Autenrieth's A Homeric Dictionary and the two-volume Iliad in the Loeb Classical Library. The other option is to begin with John's Gospel, which has the advantage of being familiar in translation. Then add Smyth's Greek Grammar and the abridged version of Liddell and Scott's Greek-English Lexicon. (Liddell's daughter was the inspiration for Alice in Wonderland.) Eventually, you will want to invest in the unabridged Greek-English Lexicon (LSJ, ninth edition). All of these books are readily available from online booksellers.
-from Ancient Greek Online.
Taking the plunge.
As to knowing Latin, I had three years of it, Latin 1 in eighth grade, 2 in ninth grade, and 3 in tenth grade. I don't recall that Hialeah High School had 4th and 5th year Latin courses. I don't believe it did. (I started Spanish in tenth grade, continued Spanish until I graduated from high school, and studied it during the first two years in college.) I didn't get back to Latin at Duke. I can't say that I "know" Latin, but the junior high and high school courses were a great help to me. I had really fine Latin teachers. I can picture them both clearly. I can recall right now the name of my teacher in tenth grade, Mrs. Joyce Horacek, but not the name of my Miami Springs Junior High teacher. All "the brains" back then took the Latin courses.