The menu at the top of each agenda includes an Edit Signups menu. Click on the link at the top, Edit Signups, to enter Edit Signups mode. (If you do not see that option when logged in, it may not be enabled for your account.)

In this mode, you can assign roles to members other than yourself or edit speech project details on behalf of another member.

The dropdown list for other members of the club includes information about when each member last filled that role (according to past agendas) and whether the member has indicated they will be absent.
Alternatively, you may type in the name of a Guest, a nonmember who will be filling a role.
Edit Signups mode also allows you to change the role count and time reserved on the agenda and to change the content of any Toastmasters Editable Note blocks (such as often used to record a meeting theme or word of the day). If a Toastmasters Absences block has been included on the agenda, Edit Signups allows you to record planned absences on behalf of other members.
Changes to role assignments are recorded automatically, but some other details such as speech project details and the content of Editable Note fields may not be.
After making all your edits, scroll down to the very bottom of the form and click Save Changes. The page will refresh, reflecting your changes.
Editing a Single Role Assignment
You can also edit a single role by clicking the Edit link that appears below it.

Click Edit to reveal an editor form you can use to change the member assigned to that role or, in the case of a speaking role, the details associated with that speech project.

When done, click Submit, and you should see a message confirming that your changes have been recorded.
Edit Signups Versus Editing an Agenda Document or Template
Edit Signups can be enabled for members who do not have the authority to edit the underlying event documents, which define the basic structure and organization of a meeting. (See: Agenda Organization).
Typically, a club defines an event template for the typical structure of its meetings, and each meeting is a separate event based on that model. These event documents specify the order and number of roles, but this data is generic. The specific information about which members will fill which roles at each meeting comes from members signing up and meeting organizers editing the agenda, using the process described above.