What is the correct way to "repot" a staghorn fern?

My staghorn fern outgrew it's wood base. When I pulled it off the base there were no roots visible or any obvious way to reattach it to a new and bigger base.

What is the correct way to "repot" a staghorn fern?
i have a really huge one that is still on a dinky little cork bark-you can just get a larger piece of cork bark-put a bit of sphagnum moss on the bark between the staghorn and the bark and use plastic wires to wrap around the fern and the bark to keep it in place. you don't need to remove these wires when the roots grow to cling the bark as the staghorn will grow new 'sterile' leaves on top of the wires. i actually used netting material from those frilly shower puffs that are used to lather soap that i bought from the dollar store and it proved to keep the staghorm very stable and once it strated growing new sterile fronds (the brown ones that grow around the base)it hid the netting completely-actually i can't remove it even if i wanted to now. just remember to use sphagnum moss and not dirt or anything like that.