Sharon...I am very familiar with buying the tickets to this tour now that I have recently bought 2 sets of the night tour for friends next month and a set of the daytime tour tickets for 4 of us on October 8.
Buy this tour directly from the coopculture website...not a 3rd party tour company.
1. The nighttime Underground Colosseum tour.
http://www.coopculture.it/en/ticket.cfm?office=Colosseum by night 2017&id=0&evento=177
These tickets are easier to obtain as they go on sale further ahead than the daytime tour. The cost is 20 euro/person, but your entry into the Colosseum is included with this tour ticket.
Right now, tickets for the nighttime tour are only available until the end of this year, so I would check every few weeks to see when they put next year's tickets up for sale.
2. The daytime Underground Colosseum Tour.
http://www.coopculture.it/en/events.cfm?id=6
These tickets are difficult to obtain because they are in high demand. They only go on sale the 3rd Monday of the month before at 9m Rome time (i.e., May 21, 2018 for all of June, 2018). The cost is 11 euro (includes a 2 euro reservation fee). This tour does not include your entry ticket into the Colosseum...you have to buy that separately (it is a combined ticket to the Colosseum and Forum/Palatine Hill).
Pros of the night time tour...tickets are easier to obtain, it is cooler and less crowded at night in June, the Colosseum lit up at night is beautiful.
Cons of the night time tour...the tour does not include access to the 3rd tier.
Pros of the day time tour...the tour includes access to the 3rd tier of the Colosseum where the views over the Forum are quite good on a nice day.
Cons of the day time tour...it will probably be hot in June and definitely more crowded, you have to go online at 9am Rome time to even have a chance of getting these tickets...tickets sell out for the month within an hour and it is often difficult to even get into the system because of the demand.
These are the parameters for buying these tickets at present. Keep checking the coopculture websiten case changes are made.