Or, when does this process affect me?
The process of nominating and reviewing $TYPE bugs is active to some degree at all times. It is particularly visible, however, after the Milestone freezes for each milestone of a release (Beta and Final). At the Milestone freeze (Beta freeze or Final freeze), the stable fedora package repository is frozen, meaning packages can no longer move from the updates-testing repository to the stable repository from which the 'candidate' composes are created.
If a Fedora milestone release is currently in a milestone freeze (you can check the schedule for the next release here) and you are a packager or tester and you believe a build of your package or a package you are testing should be in the milestone release, this process concerns you. After the milestone freeze, the build can only be promoted to 'stable' and included in the release if it fixes a bug that is granted blocker or freeze exception status.
After the milestone release is finished, the milestone freeze is lifted and builds can be marked as stable again without following this process, so if the build can wait until after the milestone release, you do not need to follow this process.