Choose a new pot for your davallia that is only 1 to 2 inches larger than the pot it is currently growing in. Cover the drainage hole with a large stone or piece of broken terracotta pot to keep the soil from washing out when you water.
Mix equal parts of rich indoor potting soil, sphagnum moss, peat moss, compost, coarse sand and orchid bark. This mixture will be used as potting soil for the davallia.
Lay the davallia in its current pot on its side on a hard surface, like a table or bench. Holding it with both hands, rap the side of the pot on the table or bench. Grasp the base of the plant with your hands near the soil line. Pull and twist it gently to remove it from the pot.
Gently tease the roots free at the bottom of the pot, if they are winding around the root ball, a sure sign that the plant is ready for repotting.
Measure the depth of the root ball in comparison with the depth of the new pot. The surface of the root ball, after transplanting, should rest about 1 inch below the rim of the pot. This will keep water from overflowing when you water the plant. If needed, add a few scoops of soil to the bottom of the pot to ensure the top of the root ball falls in the desired spot in relation to the top of the pot.
Slide the root ball into the new pot. Center it in the pot, holding the base of the plant with one hand. Add soil to the spaces between the root ball and the sides of the pot. Use a dowel to firm down the newly added soil. Add soil to a small area on one side of the pot, tamp it with the dowel, then add soil to a small area on the opposite side of the pot. This will keep the plant centered as you fill in the gap between the root ball and the new pot.
Firm the soil gently at the top of the pot with your hands. Do not cover the roots at the surface of the soil. Davallia roots naturally grow in the air and the plant will not survive long if its roots are buried.
Water the newly transplanted davallia thoroughly, until water washes out the bottom of the pot and drains thoroughly a total of three times. These three thorough waterings in close succession will ensure that the nearly soilless growing medium is thoroughly moistened but not drowning in water.
Remove and empty the drip tray beneath the plant when all of the excess water has drained from the pot.