I am looking to delve into the teachings of Rav Joseph B. Soloveitchik (1903-1993). Any recommendations on a good starting point?
I'm no scholar of the Rav, but I found the Rosh Hashannah and Yom Kippur Machzors and the Haggada based on his teachings to be eye-opening introductions to his oeuvre. They're full of references to his other published works, so if you see a passage you find particularly interesting, you can follow it up by studying the work it was excerpted from.
In my opinion the best place to start is Here:
It is simpler then the other books that have some heavy philosophy and language. They are cross referenced to his other books so if you like an Idea you can find it and the person who wrote it was a close talmid. Plus it is on the Parsha so it makes it very usefull.If you want the Plain The Rav Thinking Aloud not on the Parsha it has most of his viewpoints on the important issues and it is an easy read
There is a 16-part audio web series from Web Yeshiva given on the Lonely Man of Faith taught by Rabbi Jeffrey Saks. you can download it from here: http://www.yutorah.org/search/?s=lonely+man&series=4191 Give's a nice introduction to Rav Soloveitchik's teachings.
I strongly recommend Halakhic Man. (Some say to skip the first 40 pages. From what I have heard, people find them very tedious, as it is just a preface to the piece, and Rav Yoshe Ber uses very large words with which most people are unfamiliar, but after roughly the first 40 pages he actually gets to the premise of the essay.)
In it he describes and elaborates on the worldview and persona of the great halachists of the past. And how their approach and thought process differs from other personalities in their relation to G-d and the world he put us in.
Largely he sets down the philosophy of his family; the Soloveitchiks, and their approach to halacha and their mindset.