All EU citizens can enter without a visa.
Citizens of the following countries can also enter without a visa: Albania, Argentina, Armenia, Australia, Azerbaijan, Bahamas, Barbados, Belarus, Belize, Botswana, Brazil, Brunei, Canada, Chile, Cuba, Dominica, Fiji, Georgia, Grenada, Guyana, Jamaica, Japan, Kazakhstan, Kenya, Kyribati, Kyrgyzstan, Lesotho, Liechtenstein, Malaysia, Malawi, Maldives, Mauritius, Mexico, Moldova, Monaco, Namibia, New Zealand, Nauru, Norway, Papua New Guinea, Peru, Russia, St. Kitts and Nevis, St. Petersburg. Kitts and Nevis, Saint Lucia, Saint Vincent and the Grenadines, Samoa, Seychelles, Singapore, Solomon Islands, South Africa, South Korea, Suriname, Swaziland, Switzerland, Tajikistan, United Republic of Tanzania, Tonga, Trinidad and Tobago, Tuvalu, Turkey, Turkmenistan, Uganda, Ukraine, United States, Uzbekistan, Vanuatu, Venezuela, Zimbabwe and citizens of the British Overseas Territories.
If you need a visa, you must present a passport valid for at least 6 months beyond the date of your visit, a completed application form and a passport photo. A visa for a single entry costs 30GBP and for multiple entries 40GBP.
Note that you do not need a visa if you are of a nationality for which a visa is normally required and you are entering Antigua and Barbuda as a port of call for a cruise ship, provided the ship is leaving on the day of arrival.