I actually had a really hard time figuring out how to do blog post permalinks with Squarespace. Squarespace's forums (ironically) didn't have an answer for me. And it was only after doing some googling that I happened upon this blog post by Alex Dunner... which didn't help me... but it did contain a link to this post by James Smith which had the solution I was looking for. Phew.
Basically you just have to add this as a footer to each post:
Via this this settings panel:
Not super complicated, but also not super obvious. It's also not the optimal solution (I'd prefer the link appear near the title of the post) but it'll do for now.