I wouldn't both with peat moss, but just buy a bag of top soil from Home Depot (about $1) and amend the new area with that; it's got enough organic matter in it to be of help. Get the new spot ready before you dig up the ferns. Then just dig around the ferns in a generous circle and about 8 inches down. Both lady and ostrich are very hardy ferns and should take the transplanting well. Even if you damage a frond or two, new ones will grow.

I have found the smaller ones that are just breaking ground take the move better. The large ostrich can look pretty ratty if you bend or break a fron. They will be beautiful, next year but at this point in the spring, why look at that all summer if it can be avoided.

If they are ostrich ferns, don't worry too much about the soil--they will do well just about anywhere as long as the soil doesn't dry out too much.

Ostrich ferns transplant easily, although the smaller the better. Late fall and early spring are best but I've discovered that you can cut all the foliage off and transplant the crown without leaves. It will suffer less shock this way, and will grow a new set of leaves as long as you don't do it too late in the growing season.