Select an area of barren ground for your moss. Paving slabs, concrete and rocks are all suitable. Moss can grow upon such surfaces, but few weeds can. If you want a more ornate moss garden, arrange large rocks in a way you find appealing. Flat rocks in the gaps provide another surface for mosses that weeds cannot colonize.
Select one or more types of moss from elsewhere in your garden and remove a small amount. Preferably, select mosses that are growing on a similar surface. If you choose mosses growing on wood or soil, provide extra nutrients and moisture later on. For a moss garden, select several different types for variety. For groundcover, select a species that appears to grow rapidly.
Tear the moss into little pieces and blend briefly with a pint of yogurt or buttermilk and a pint of water. A little fertilizer is optional but helps, especially with soil-growing mosses. The mixture should be full of moss spores, and the other ingredients provide moisture and nutrients. Pour the mixture into a bowl, take it to the site and paint it liberally on the surfaces.
Mist the surfaces daily. Moss needs moisture.
Add a small amount of general-purpose organic or inorganic fertilizer to the water for misting once a week. Use a little less than the packaging recommends for most plants.
Remove stray weed seedlings as they appear. Although a rocky or concrete surface is inhospitable to weeds, they might briefly establish themselves among the moss.