It is easy to start accept bookings from your clients at your SquareSpace.com page. You will need to have an advanced or business subscription with them but then you can simply create a new page and follow the instructions in this link:
http://help.squarespace.com/guides/using-simplybookme-with-squarespace
If you only have a free subscription with them, then you can only add a menu link to your booking page at SimplyBook.me by creating a new page, select that it is a link, and insert the link to your booking page.