The Roman Forum was the second part of my combined Colosseum and Forum ticket that cost €18. This also includes Palatine Hill and some other small areas. The information is all readily available on the tickets that I booked online. As far as I understood the tickets allowed for entry to the Colosseum once and then the Forum within the next 24 hours. Don't quote me on that though.
The attraction is a mix of a large open air museum and gardens. There are some buildings to enter but it is mostly outside. Take a hat and some food. There are water fountains for hydration, if you have a bottle to fill.
The prettiest areas are up on the highest levels. You climb a ramp through a large building and come out in a very pretty area of gardens and an orangery. I'd never seen an orange tree before, and you could smell the citrus in the air.
The views from up top were wonderful, offering some great views of Rome. It was a very tranquil place, despite there being quite a few people about. I found I was still able to find some areas away from quite so many people.
On the way back to the exit you can see Circus Maximus from above and there were parakeets flying about in the trees in the SE of the forum.
Sadly, I thought the queues for the forum were worse than those for the Colosseum. I entered near the Colosseum and was queueing for what felt like an hour. There are other entry points though so perhaps you don't have to queue that long.