The TV show 'The Vampire Diaries' actually pulls most heavily from the first three books in L.J. Smith's series: 'The Awakening', 'The Struggle', and 'The Fury'. Once you get past that, the series and the books just completely diverge. They basically used those initial concepts—the Salvatore brothers, Elena as the popular girl, the love triangle—as a launchpad and then ran in a totally different creative direction.
After season one, the showrunners were basically writing original stories that had little to do with the later book plots, like the kitsune mythology or Elena becoming a vampire so early. It's fascinating to compare, but if you're looking for a direct adaptation of books four through, I think, thirteen? You won't find it. The 'Legacies' spin-off is even further removed, though it borrows character names like Hope Mikaelson from 'The Originals', which was a show-only creation.