There is a ton of great information from the Canvas Guide about starting a discussion.
One thing we have found in the Shakopee implementation of Canvas is that since all the sections of your course are together as one course, starting a discussion defaults to including all your kids (all sections) in one discussion. There is currently only one known workaround for this, which is to make groups of your kids for each period.
You will only need to do this process once, since once you have groups you can always assign discussions to the groups. Click on the People section of the left sidebar when in your course (even if it is greyed out). You should see two tabs at the top; Everyone and project groups. If you don't see project groups or would like a different group name, click on "+ Group Set" and add a group.
Once you have a Group Set you would like to edit, click on that tab.
In the Group Set section, you now need to add groups by clicking on the +Group button. This allows you to create groups like Period 1, Period 2, etc.
After you have created your groups, when you click on the + sign next to a student name you can add them to a group. You will need to have a roster handy, as the students are listed by alpha, not by section. Add all your Period 1 students to that group, and so on.
After creating a group set, you can make a discussion that automatically groups students via that set. Simply check the "This is a Group Discussion" box and make sure the correct group set is selected.