Citizens of the EU member states, as well as Iceland, Norway, Liechtenstein and Switzerland, may stay in the Czech Republic and work here without a special permit. A valid travel document (passport or national identity card) is sufficient. However in some situations you must report your residence to the Czech authorities - please see below for details.
What to do when you arrive:
Within 30 days of entering the Czech Republic, you must report your presence to the appropriate Foreign Police Department nearest to where you are staying. This obligation does not apply if the person providing accommodation (hotel, hostel, student residence or similar establishment) submits the registration forms on behalf of you.
If you change your address, surname, marital status, or data data contained in the travel document, you must inform the Foreign Police of this.
If you are staying more than 3 months in the Czech Republic, your presence must be registered with the Foreign Police within 30 days (see "staying 30-90 days") and in addition, you can (although you are not obliged to) request a certificate of temporary residence.
This is highly advisable because it will enable you to obtain a "rodné číslo" which you will need for many other administrative procedures during your stay.
All changes (address, marital status, purpose of stay, passport) must be reported to the Foreign Police.