Tolkien never wrote a dictionary for any of his languages. He did write a lot about the subject, but that's dissipated throughout
The History of Middle-Earth, which covers the period c.1915-1973. As one might expect, he made a lot of changes to all of his tongues during that time, even after the publication of
The Lord of the Rings. I suspect that all of the various courses available on the web are based on the HoME, so they're probably the quickest way to acquire some conversational Sindarin.
If you really want to do things the hard way, I suggest beginning with the vocabulary in the back of
The Silmarillion and working your way into HoME with care, bearing in mind that the earlier vocabularies and etymologies have been superseded. Other useful sources are the poems in Sindarin and Quenya for which Tolkien provided translations, several of which are contained in his lecture and essay
A Secret Vice. This concerns the whole subject of invented languages and is published as part of a collection called
'The Monsters and the Critics' and Other Essays (HarperCollins, 1997).
All I can say in conclusion is 'Good luck'.