Most of what agencies actually do to you happens through rules — and rulemaking follows a public process designed to let you weigh in before a rule ever binds.
An agency can only make rules Congress has authorized it to make. The enabling statute sets the boundaries; a rule that strays outside them can be struck down.
Under the Administrative Procedure Act, the agency publishes a proposed rule in the Federal Register, opens a public comment period, then publishes a final rule that must respond to the significant comments it received. This is why the Federal Register matters: it is where the public square for rules lives.
A final rule can be reviewed in court for exceeding the statute, ignoring the record, or being 'arbitrary and capricious.' Congress can also overturn a recent rule by joint resolution under the Congressional Review Act.
Every proposed and final rule appears in the Federal Register — the same official feed that powers the 'recent actions' list on each agency's page here. Following an agency means following its Federal Register output.