I've never tried it, but I would think you would plant the seed, water
it, then cover it with cellophane wrap until it germinates. Remove the
wrap then. Most grasses have to have a lot of sun, except maybe fescue.
I recently bought a pack of "cat grass." It looks to me like just
plain wheat in the pack.
She might like cat mint, which is an herb that cats really like. It is
very easy to grow indoors. You can buy the little packs of seed
anywhere.
Good luck! Let me know how the grass-farming goes.

Sherry

I buy the "cat grass" seed packets at the pet store, it's really just a
mix  of barley, oats and wheat seeds. I use an 8 in. clay pot, filled
with potting soil from the hardware store, cover the seeds about an inch
deep, put in a sunny window. In the winter seeds sprout in about a week,
in the summer in about 3 days. I used to use smaller pots but the grass
usually grows better and survives longer in the large pot. 2 or 3 times a
year I end up dumping the whole pot out and starting over with fresh dirt
and seed.  

We grow the cat grass pretty much the same way 5cats does. But as you
mentioned it comes up fairly thin.

Cali also waits at the back door for her daily supply of Catnip.

You can buy wheat, oats, etc. from feed stores - provided you live
where they are.  Use feed, not seed - seed grade tends to be coated
with toxic chemicals for fungus control.

I used window boxes a foot or so under fluorescent lamps. Hardware
cloth box-like covers with bamboo skewers protruding from many of the
holes keep the cat out of it until it's ready.

On a smaller scale and with less access to seeds, you can use popcorn
sprouts: wrap popcorn kernels (not ones from a microwave pack, use
those packed in a jar or plastic bag (jar ones tend to work better))
in paper towels, leaving a path to the top for the shoots to grow.
Wet the paper towel and roll it up to fit in a jar.  Put the jar on a
window sill and wait not very many days.  When the shoots are 6-8
inches high, cats just love them - cut them off and discard the paper.