People tie it with fishing line (my favorite option personally) or use super glue generally.
If you tie it, you want to tie it tightly, because the more moss in contact with the wood the more moss will grab hold of the wood. Eventually, the moss will grow over the fishing line as well, making it impossible to see.
The bottom parts of the moss will die if they don't get enough lighting, but you could always trim the moss when it gets too bushy to help prevent that from happening.
However, unless you are dosing your tank and have high lights and co2, it might not grow super quickly.