If at least one parent is homozygous for the blue egg gene, then all of their female offspring will lay eggs with blue shells (either blue or tinted to green on the outside, of course) and all of their male offspring will carry at least one blue egg gene. If both parents are homozygous for the gene, then all offspring will be as well.
The blue egg gene I believe is designated as O, where O/O is homozygous for blue eggs, and o+/o+ is homozygous for not blue eggs. An individual that is O/O always passes on O no matter what the other parent has. So all offspring from such an individual will be O/(either O or o+ depending on what the other parent passes on).
If you've hatched a lot of chicks and consistently gotten green egg laying pullets from your rooster crossed to brown-egging hens, then it's a pretty solid assumption that he is homozygous for blue egg shells.
However, the hen is not a given, as you recognized. A hen that is O/o+ will also lay blue eggs. Some say that O/O eggs are a deeper blue than O/o+ eggs, but there are other genes that could change how deep of a blue color those shells are, even when a hen is O/O, so a lot depends on the hen's background as well. If she's a pure breed like an Ameraucana or Legbar, it's pretty likely she is homozygous O/O for the blue shell gene.
