I've wanted to learn Latin for a while, and decided that there's no better time than the present. Are there any really good websites that make the process easy and quick? How long might it take to learn a decent amount of Latin?
Same for American Sign Language. I've recently befriended a deaf person, and have been slowly learning ASL, but would like to speed up the process and tighten up my fluidity. Any help there?

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The other contributors provided great resources, but if you really want your learning to be easy and much more efficient, why not take lessons from an online tutor?
I know a website that has a wide range of tutors for many languages: http://edufire.com/ Lessons are one-on-one, done using a webcam and the prices are more than convenient.
Check out tutors for ASL: http://edufire.com/tutors/american%20sign%20language%20(asl)
and also for Latin: http://edufire.com/tutors/latin
As for how long it might take to learn “a decent amount” of Latin, that depends entirely on how quicly you are able (and also willing) to go. I think it is generally possible to cover the morphology of all the parts of speech in around 16-17 sessions, with other 3 or 4 sessions dedicated to the basics of syntax. After these, a student should be able to read and translate simpler texts. Of course, translation practice is the most important thing and the only way to become able to undertand more complex texts.