There are two quick ways.
First, check towards the edge of the spine where the pages end. If you can see individual signatures (little bundles of pages all stacked on top of one another), then it’s sewn. See below:
Another way to determine if it is sewn is to open the book and look deep into the pages and see if you can see little points or holes. This is where the threads are passed to through to stitch the signatures together. See below:
If your book has a glued binding, you will not see those individual signatures near the spine. See below:
And again, looking into the pages as before, you will not notice those little holes, just a smooth edge where the pages meet This is a sign of a glued binding. See below:
This is just a quick method of determining what sort of bindings you have on your bookshelf.