Notice period — the time between giving your resignation letter and your last day of work. The minimum is 2 months.
Main change: counting from the day of delivery
Before, the period started on the first day of the next month. Now, it starts from the day you hand it over. In practice: if you hand it over on May 5th, your last day is July 5th, not July 31st.
This changes planning for both sides. If you thought you could "work until the end of the month plus two months" — this is no longer the case, and no one will pay you for an imaginary extra week.
Shorter period
For certain organizational reasons for dismissal under § 52, the notice period is 1 month instead of two. You should check the current version of the law for the exact list of these reasons — sources explain it differently.
What else
When you are dismissed for organizational reasons, you most likely also have the right to severance pay (odstupné) — 1, 2, or 3 average monthly salaries depending on your length of service. This also applies if you sign an agreement (dohoda).