A quick search pulls this up.
http://www.iuoe825.org/home/join/apprenticeship/
As it says, apprentices are taken on an as needed basis. This is based on retirement, work, and need projections. They will not take more apprentices than they can handle. Basically, they need to make sure there is enough need to get apprentices through their required hours in a timely manner, and not starve trying to do so.
Of note, prior experience will be of no consequence, and will not give you any preference. The Department Of Labor has requirements for apprentice programs of all trades. It will be a points based system. First thing you usually do is take what is the equivalent of a GED knowledge test. Once you are completed with that, there will be other things, some of which may be an industry related test. This is a points system in the name of "fairness." It is established so there is no preferential treatment to members relatives. It is also established to meet certain diversity requirements set forth by the DOL. There are only a few ways to get additional points in these systems, The first is to be a US Military veteran. The second is to be a minority, be that sex or race based. Third, not positive on this, may be the amount of times you have applied to the program, meaning you applied for this year, and did not make the cut, you came back at the proper time and applied for next years.
Contact them via the information provided on the site link. They will have a rough idea on when they expect their next apprenticeship "class" to begin the process. Im glad you are interested, there are not a lot that are interested in the trade these days for the right reason. I see many who see the big dollar signs, and think its just like a video game. That type ends up being mediocre at best. They water down the trade, and they tend to be the type of members who are willing to overlook contract requirements to keep working. These deal cutters undermine everyones working conditions over time. They all jump at the opportunity to save their skin. Unfortunately, the contractor then expects everyone to accept that deal. Simple as this, Top notch skills you gain from training and time in the machine, uphold your end of the contract, expect the same from the contractor, and Ill be proud to call anyone that does that brother, or sister.