You didn't say, but I'm going to assume you are part-time, non-management; and in the USA.
For most of the country, it will be 1 year after you started (so next June). Some areas get it after working a minimum # of hours in a given time period (something like 250 hours in a 3 month period).
Best thing for you to do is ask some coworkers who have been there at least a year when they got it. And find out if there is a union shop steward for your shift. Your benefits eligibility is covered in the union contract. There are many regional/local supplements/riders so answers to your questions depend on where you are.