Here is my setup...

To start with, i layer strands of fissidens on pieces of coconut shells (didn't bother to manually tie them on, the fissidens will eventually root in and attach on their own anyways) and then add abit of water into the container.
I prefer to use coconut shells as the base as they have a more natural curved shape once the fissidens establish (like small green hills), compared to using steel meshes which tend to create a rather flat artificial look.
This process is sort of like a "dry start method" (aka DSM) whereby the plants are grown emersed for a while before being submerged. The bottom layer of water will naturally wick up the coconut shells to keep the fissidens hydrated during this period of time.
The containers i use are just transparent IKEA plastic boxes. The lids are kept closed at all times to retain high humidity in the container (very important for fissidens undergoing DSM) and also to prevent mosquito breeding.
In the photo above, the top container has fissidens growing on coconut shells, while the bottom container has loose fissidens just grown floating in the water. The containers are stacked up to save space.
After 1-2 weeks, once the fissidens attach to the coconut shells, i fill the container with water and they will continue their growth submerged.
On a weekly basis, i do a full water change with de-chlorinated water, no fertilizers added. So far, i've not spotted algae in any of the containers, even in the presence of direct sunlight. Most likely the limited nutrients available are all used up by the fissidens and the sealed environment probably helps prevent external contaminants/spores from being introduced too.
Here is a batch showing the growth rate after around 1 month...
As you can see, there is "pearling" (excess oxygen bubbles from active photosynthesis) even from the fissidens... sunlight is a very powerful light source indeed!
Due to direct sunlight exposure and the covered container environment, the water temperature in the containers can often times reach 31-32°C, but interestingly the fissidens didn't seem to show any signs of deterioration and instead seem to grow even faster and greener (compared to my indoor tanks), so i guess fissidens can adapt and thrive in high temperature conditions too.
Looks like growing aquarium plants outdoors can be a useful method to cultivate them... sometimes even better than growing them indoors. :)