Usually your copyright work will be protected abroad automatically in the same way that it is protected in the UK.
The UK is a member of many international agreements including the Berne Convention, where the national law of each country automatically protects copyright works which are eligible for protection, under the rules of other countries who have signed these agreements.
Most countries, including all western European, the USA and Russia, now belong to the Berne Convention. Under this agreement, you do not have to mark your work in any way for automatic protection to apply. However, it is sensible to mark your work with the international © symbol, followed by the name of the copyright owner and year in which the work was created.
The USA does have an official register of copyright works, although registration is not actually needed to qualify for copyright protection in the USA (or indeed any country that is a signatory of the Berne Convention).
Protection abroad can also arise from obligations in the Trade-Related Aspects of Intellectual Property Rights (TRIPS) agreement. This forms part of the World Trade Organisation (WTO) agreement and may protect your work automatically. Details of the TRIPS agreement and a list of these countries are on their website.