The Schengen Zone is a group of countries who have removed border controls between them, and the Czech Republic joined this group in 2008. This means that those passing between Schengen Zone countries will not be checked at the border, although the countries still have the right to request documentation from those entering the country if they want to. Third state nationals most have a valid passport to enter any Schengen member state. Having a long-term visa in the Czech Republic does not grant the holder the same rights of travel and stay as a citizen of an EU or Schengen member nation. This is because some countries are members of the EU and not the Schengen Zone (such as the UK), while other countries are part of the Schengen Zone and not the EU (such as Norway, Liechtenstein, Switzerland and Iceland).
Travellers from countries within the Schengen Agreement must carry a passport or ID still though, as domestic policing laws are not affected by the Schengen Agreement and authorities could demand to see documentation at any point of a stay. It is the case that passports could be checked in Austria, Belgium, Germany, Hungary, Portugal, Spain, Slovakia, and the Netherlands, while photocopies of passports are accepted in Bulgaria, Estonia, Latvia, Romania, and Slovenia. In the Czech Republic it is necessary for visitors to carry some sort of ID at all times and the police can request to see this at any time.
When it comes to the length of your stay, regardless of whether you have a long term visa or Czech permanent residence, the duration in another country that’s part of the Schengen Zone is the same: 3 months in a 6 month period.
If you have permanent residence in the Czech Republic, you are allowed to spend 3 months out of 6 months in another Schengen State. When this period is over, you don’t have to return to your home country; instead, you can return to the Czech Republic and your stay in the Czech Republic won’t count against your stay in the rest of the Schengen Zone. You are not allowed to work though and you will need medical insurance for the entirety of your stay.
If you intend to stay for longer than 3 months, you will need to apply for a special Schengen visa. The UK and Ireland are not a part of the Schengen Zone, so different regulations exist in these countries. When it comes to the UK, citizens of the USA, Australia, New Zealand and Canada are allowed to stay for up to 180 days without a visa. Visitors to the Republic of Ireland are also allowed to stay for 180 days without a visa.
There is one thing that can change the residence requirements mentioned above, and that is if you have a family member who is a citizen of the EU. This includes a spouse, a partner in a civil union or a parent. If a spouse moves to another EU state, you will have to apply for a “family permit” and to apply for this you will need a passport and a valid marriage certificate or proof of partnership.