For travelling to Monaco, you need valid passport or identity card. Since 1st January 2006, latest version of Travelling Documents Law is valid (No.559/2004). According to this, you can use for travel purposes your identity card only, including readable data.
According to declaration of Interior Ministry, the identity card is a document for its holder only. So, it is not recommended, that citizen of Czech Republic, younger than 15 years of age, travelling together with their parents, registered in parents´ travelling documents, could travel with this registration only. This person needs to have his own passport, too.
When travelling by car, Czech driving licence is sufficient. Nevertheless, when you use rented vehicle, you need to have international driving licence available. Even so called Green Card is required.
Information and warnings on travelling abroad is to be found HERE.