Looks like the variety of Boston fern (Nephrolepis exaltata) known as 'Curly Locks', although pics are not clear enough to be sure.

The biggest issue with growing ferns indoors is maintaining proper humidity - it isjust too dry inside most homes to keep ferns happy. This info sheet on growing ferns, both outdoors and as houseplants, should help.

btw, old fronds do yellow, brown and dry up and die from time to time so that's to be expected. However, I do believe yours has more of a water/humidity issue than just the natural shedding of old fronds.