There is more than one plant commonly called irish moss. (and one is a seaweed, let's assume that isn't what you've got)

Two -

Sagina subulata , Surface sow at 20ºC (68ºF) in light, germinates in less than two wks

Minuartia - treat the same as above, but if no germination in 3 - 4 weeks, move to 40F for 2 - 4 weeks.

Ok that sounds easy enough. I tell you I was almost tempted not to mess with them cause the seeds are small! I will get them sowed tomorrow.....

I've grown Sagina subulata. My source was Pinetree. The first time around I had success, the second, nothing grew.
All I did was fill a clay pot with the potting mix, sprinkle the top with all the seed and close it up in a baggie. It grew slowly. All of it together topped one pot. It flowered the second year and died off. I know S. subulata is suppose to be perennial from what I read, but it has always been a biennial for me.

Oh I hope its a perennial for me! Like i said I was almost tempted not to mess with them cause the seed is so small, but I do like how it looks.......

Don't be put off by the size. Take some moist but well drained potting soil, sprinkle it all on the top of a pot, tie a baggie around it and keep it close at hand so you can watch it. I can't tell you how long it took to germinate anymore.
I've also bought Sagina and even those died after flowering. If I try again, I will cut off any flowers I see. However, I have plenty of natural moss around. I don't really need it. I haven't tried minuartia yet.

I'm unclear from the postings above. I would like to stsrt Irish moss from seed and am wondering if one can simply sow the seeds in the the desired area and expect success. The area in question is on the east to northeast side of the house with some shading.