Here is a pictoral version of how I harvest my BBS. I use a completely DIY system (I buy the eggs of course) and used to do the messy bright light with turkey baster thing, but this way is sooo much easier, more efficient (you get more shrimp) and cleaner (both water and empty shells).
First, I hatch the BBS in a 2L pop bottle set in the aquarium I put an air tube in right to the bottom and keep the eggs moving and I also keep a light on them. I hatch for 24 hrs or so (make a batch up after feeding at night, then harvest that batch the next night).
Once the hatching is complete, I harvest. First off, I took a 2L pop bottle and cut the bottom off. I took the cap off and drilled a small hole into the cap and, using aquarium silicone, "glued" a long piece of airline tubing into the hole. I made sure the airline tubing was flush with the inside of the cap. Next, I took a second 2L pop bottle and cut the top off. This is my "base" that I set the first pop bottle into for stability. I cut a tiny hole in the side bottom of the "base" for the airline tubing to come out through. In the first picture, you can see my setup; the second is a more close-up view of the harvesting pop bottles.


I make sure the airline tubing is tethered higher than the harvesting bottle so the brine won't flow out the tubing until I'm ready for it.

Honorable mention to Mutant, my cat. He loves it when I look after the fish because he's always in my face the whole time. This is 'his' room I have the fry tank in!
So now, I pour the brine and BBS into the harvesting bottle. The person I got this whole idea from doesn't hatch in a separate bottle; he hatches and harvests in the harvesting bottle using the airline tubing to pump air into the bottle during hatching and then removes it from the air pump to harvest. I just personally found this way easier so I don't have to keep removing the tubing from the base bottle... Besides, how much does a 2L pop bottle really cost? (about 5 cents around here...)

I like to put the airline tubing which is close to the harvesting bottle over a piece of white paper - allows for more reflection of the light. You should be able to see some of the brine move into the tubing - but not too much; adjust the height of the end of the airline tubing to keep only a few inches of the tubing filled.

Lastly, I place a light-tight cardboard box over the bottle with the airline tubing coming out the bottom. I found the P+ cracker box fit just about perfectly over the 2L bottles. I cut the top flaps off, made a little nick in one side to set over the tubing and place it over the bottles. I put a bright light over the white paper and leave it for an hour or two.

So now I've had supper, cleared away the dishes, probably watched the news... time to feed the fry. When I come back I see the peachy colored BBS swimming away in the airline tubing over top of the white paper. You can't see many in my picture because I'm only hatching a very tiny amount - I'm only feeding about 15 fry right now. When you hatch a regular amount for a large spawn, you'll see them clearly.

Now, I filter the BBS from the brine using a coffee filter placed in a dollar-store funnel, catching the effluent from the funnel in a cup. I place the end of the airline tubing in the filter/funnel, then lower the funnel below the level of the harvesting bottles. The brine with the BBS in it flows quickly out of the tubing into the filter. I usually run at least the length of the tubing of brine twice in order to get all the BBS out of the tubing. Most of the shells are still remaining in the harvesting bottle while the BBS are in the filter. I rinse them off with fresh water (R/O because that's what I use in the fry tanks), then either rinse the filter off into the tank (Or a bowl) or gently float the filter face down on the surface of the water and rinse it off that way.

I drain out the remaining brine, back into my hatching bottle, add the filter effluent to the bottle, add more BBS eggs and start all over again. I rinse out the harvesting bottles and airline tubing - if you drain it out through the tubing, alot of the shells stay stuck to the sides of the bottle and it keeps the brine cleaner that way.
And voila, happy fry, clean workspace, and easily accomplished