Visiting Roman Forum, Palatine Hill and Colosseum by goodfish
These 3 sites should be visited on the same day as they're in the same area and covered by one ticket price. To avoid the frustratingly long lines at the Colosseum, buy your combo ticket at the Palatine Hill ticket office (probably the shortest line) on Via di S. Gregorio 30. You can then choose to visit all three sites in any order you wish. As many visitors only want to see the Colosseum - or go there first to buy their combo ticket - having a ticket in hand will allow you, after a brief security check, to skip the long line and go to the shorter one (to the left of the long line). Tickets cost either 9 euro or 11 euro depending on special exhibitions at the Colosseum.
If wanting to know what you're looking at, you'll need to either sign up for a tour or bring a good guidebook as you don't receive any info with your ticket and there's no signage explaining what a particular ruin is and why it's significant. Audioguides are available for rent at the Colosseum (4 euro).
Bring water and sunscreen and wear the most sturdy, comfortable shoes you own as you'll be covering a lot of uneven ground and climbing steps! We did Forum first (it was free until March of 2008), then Palatine and then Colosseum as the latter afforded a little shade during the hottest part of the day. Then it was off for a sit-down and a cocktail in the park - see my Pavilion Bar tip under Things to Do.