The Colosseum is definitely one of the most amazing structure I've ever seen, especially when you stand in front of it and you think that it was build 2000 years ago, it's massive and beautifully done, going is is a bit expensive but not too much, if I remember right around £30, but once in if you don't have a guide you really get lost, because it is ruined and it is difficult to understand what was what and where, so I highly recommend going in with a guide or audio guide.

Buy a carnet of tickets from the ufizio di turismo and the cost won't bother you.
This is Allegedly one of the earliest concrete buildings in the world. If you're into structural engineering look at the structure and entrance ways - compare to modern stadia. Very similar. ( Except more Health and Safety worries these days)

Easy to get to, easy to find (hard to miss). Use Public Transport.

Be impressed at the effort that went to make this great amphitheatre. Every seat has a great view!

It brings you close to people and events -
Imagine the spectacle, the crowds and the blood in the arena.

Marvel at the mechanisms under the arena which allowed prisoners, animals and gladiators to enter the arena.
It really gets your imagination going..
Well worth a couple of hours on a warm Roman Morning. Remember, it's in the middle of Rome!
So go by train and bus!
Take a bottle of water with you ( its much cheaper), and treat yourself to a gelato on the way out.

I overheard one person complain that "its just an old ruin", so be prepared to see it for what it is, and imagine what it was. Afterall it is the bet part of 2000 years old. Don't stop at the Rome colisseum, don't forget to go the the palatine and the temple of Saturn, the caracallan baths, the forum and the Pantheon ( Really Amazing) and when in Rome, don't forget to do as the Romans did.