Years later I taught the same course at the university myself, and used the same experiment with my students. It requires some labour from the teachers, to purchase the animals and keep them alive, but the experiment itself is simple. I used the procedures described by Leland Stanford Junior University, with some minor modifications. We used the local species of sea urchin; Northern Sea Urchin/Drøbakkråkebollen Strongylocentrotus droebachiensis, and the local sea water temperature. This actually made it easier for us, we could use the fridge as an incubator. The temperature is crucial, if it is to warm, the urchins spawn before you can start the harvest and if it is to cold, the gonads are consumed by the urchin itself. This species naturally spawn in spring. To get the animals you either have to scubadive for them, collect them at low tide or get them from a local sea water aquarium.
When performing the actual fertilization, you need to be patient. The embryo forms quickly, but you have to wait patiently for the cell divisions. The species we used needed 2-3 hours before the one cell became two, and so on. It varied a lot between the individual embryos, but it is worth waiting for, to see a cell split into two and two split into four. There is nothing like it!
Leland Stanford Junior University has an extensive website with all the information you need to try the experiment yourself, called Sea urchin embryology. On their pages they write
Gametes of sea urchins yield exceptional experiences in the classroom; teachers and students alike are riveted by being able to observe fertilization, cell division and embryonic development. The gametes are easy to use, the developmental stages are readily seen with the microscope and the rapidity of fertilization and early cell divisions allows the student to ask questions and obtain answers within the bounds of a normal classroom schedule.
They have also started making an virtual lab site. Although it is not completed yet, there are plenty of high quality activities there. The site is called Virtual urchin website (requires Flash), and is also linked from the mothership.