What is the best way to go about learning Latin and (Ancient) Greek?
start off by not doing that
>>8188392
Alright, and then what?
>>8188401
Continue to not do it
A comprehensive textbook that gives you lots of practice with translating real Greek, plus descriptions and explanations of grammatical concepts (as opposed to any kind of intuitive method). Perseverance, not getting discouraged when you fuck up or don't understand something, a willingness to use Google and ask questions.
Instructors are mostly for answering tricky questions when you get confused, and riding your ass to make sure you keep at it. If you can do both of these yourself, you can teach yourself. Many have, for centuries.
I like Shelmerdine's Latin (but many don't). Wheelock is OK. Cambridge doesn't explain concepts enough for my liking, but it gets used a lot in college courses. Lingua Latina Per Se Illustrata is a meme. Some guy mentioned the Yale Latin course (?) recently on /lit/ and it seemed pretty good, maybe worth a look. There are also older textbooks.
For Greek, you basically have Hansen & Quinn (pirate it, hard + expensive to find in print), which is very had and very heavy on morphology and drills for the first 500 pages. Athenaze is garbage from what I hear. JACT Greek 2nd edition seems OK, but I hear complaints about it as well.
Do Latin first. It's much easier in the textbook phase and most of its concepts you will reapply to Greek, making the latter much easier. It's possible to do both at the same time, but try Latin out first.
Once you get up to a good level, or finish the textbook, dive into graded and annotated Latin/Greek readers of easy authors like Caesar and Democritus/Xenophon. Don't worry if it's rough and slow going at first. The textbook can only give you so much. If the textbook was the skeleton, then the real meat of learning begins by slowly building your comfort level in reading the actual language.