Generally speaking, you will need to create a plugin to accomplish the connection and manipulate data. It looks like Canvas uses JSON in their API. There is a good overview of handling JSON in PHP – the rest you will probably need to piece together from Canvas’s API documentation. Before you get started, make sure both sites are running over HTTPS so you don’t expose any sensitive information.
Since there are no Canvas-to-WordPress-specific tutorials available, you might also find it helpful to go through Google’s OAuth 2.0 tutorial for practice in connecting using OAuth, and then work on connecting to Canvas. In my experience connecting is the hardest part. From there, piecing together requests becomes easier.
Out of curiosity, why is the client asking you to build a WordPress site that manipulates Canvas data? I work in higher ed and would love to hear more about their use case. Are they trying to provide a different front end for faculty?