Decide how you want to see the Colosseum. Taking a guided tour is the most popular option, but it is also possible to visit the Colosseum when it is hosting shows. These can be expensive, due to the small number of seats available. If you are interested in seeing a show, research when these are on and book your trips around these dates.
Travel to Rome. From Europe, there are plenty of trains into the Italian capital. If you're coming from outside the continent, Rome has two large international airports, Leornado Di Vinci and Ciampino International. Both offer flights from most of the world. From the airport, there are taxis and a shuttle bus service to transport you into the middle of Rome, where the Colosseum is among numerous tourist attractions. The Colosseum is located next to the Palatine, and the Imperial Forums.
Purchase your tickets--you can use online services to pre-book if you know the dates you will be visiting. As of October 2010, the Colosseum is open every day of the year, excluding Christmas Day and New Year's Day. It opens at 8.30 a.m., and closes at between 4:30 and 7:15 p.m., depending on the season. EU citizens under 24 or over 65 are entitled to a discount, and children who are being carried or are in a pushchair can enter for free. If you book online, you'll be given an entry voucher to print, which will be checked at the ticket desk.
Spend the day exploring the architecture and listening to your tour guide, if you opt for a guided tour. You'll see the Colosseum as it looks in the daytime, and also as the sun begins to set--it's an amazing sight.