Resources
Teaching: The Rice University Center for Teaching Excellence is a great resource.
Postdocs: If you are hoping to continue in academia, you will likely apply for a postdoctoral position. Here is some very basic information to get you started, but you should also be communicating regularly with your advisor about the process. In addition, I will organize a panel in the spring for those planning to graduate the following year.
Internships: If you are considering a career outside of academia (or even if it hadn't occurred to you) an internship can give you insight into other opportunities for your future as a mathematics PhD. Some links to programs you might consider:
The Department of Energy's 17 labs with internship opportunities.
Note: These are paid internships (often well-paid), and I am inquiring about potential conflicts with stipends.