I'm assuming you already have insulation and a support panel in place on your roof's structural beams.
Now, the function of the first layer you add is to make the roof water- and rootproof. Personally, I think the best sealing is simply one layer of EPDM which you can order in the larger DIY stores (at least you can here in the Netherlands). You simply glue the EPDM to your roof. This site (no affiliation, just like the videos they host) has all the info on how to apply it. Alternatively you can use bitumen but this is more difficult to DIY and won't last as long as EPDM. Never use zinc, which is not very sustainable anyways.
Some people like to add a protective and/or root-repellant layer on top of the first layer, but in my experience that is not really necessary when you have a good and solid first layer.
Layers of a green roof (source)
Next comes the drainage layer (3rd layer from the bottom in picture above). It's purpose is to both hold water and drain superfluous water. On our green roof the drainage mats were included in the package with the growing medium and plants. I'm not sure if you can buy it separately, but it looks something like this.
You can place a filter fleece on top of the drainage layer to prevent it from clogging. We did this on our roof, but I know several people who didn't and their roof seems to work just fine without it.
Now you can add the growing medium and vegetation. Don't forget to place pebbles or stones along the edges of the roof to allow drainage and to make sure that the vegetation won't start growing to places it is not supposed to grow (see for example picture below)