Starting seeds for your aquaponics grow beds depends on the substrate you are using. See this entry for options. If you use vermiculite on the upper layer, you can just spread small seed on the surface and cover with a thin layer of more vermiculite. Larger seeds can just be embedded in the vermiculite. If you are using Hydroton, you can also embed larger seeds like beans just under the top layer.
For small seeds in Hydroton, or for more controlled planting in any media I prefer to use coconut husk pots with a vermiculite media. I can germinate the seed either indoors or in the greenhouse, and then put the entire pot into the grow bed when ready. This can be used in any media grow bed, including Hydroton.
The benefit of this technique is that you are not introducing organisms into your ecosystem that may be present in regular soil, you have control over the planting, and you can germinate the seed in optimum conditions for the appropriate seed.