I had read on here some other poster's setups for sink drains, and went to Home Depot to setup similar, but ended up doing mind in a different fashion that I think will be pretty easy for most folks with basic DIY skills to do.
In my basement, we don't let the cats into the utility room with the washer/dryer, but they are allowed in the rest of our mostly finished basement. The install location is then about 10 feet or so from the cold water & utility sink and on the other side of a wall, so I needed to both 1) hook the waste line into the sink drain plumbing and 2) extend the hoses.
Here is the other install that I drew inspiration from: http://www.litterbox-central.com/litter-box/catgenie/topic1015.html
But when I went to Home Depot, I found this part below (used for dishwasher drains normally) which meant that I did not need to do ANY plumbing changes besides replacing the very top piece of the existing drain setup. It screws into the drain at the bottom of the sink, and just slides into the first part of the "p-trap." Since the part is 8 1/2" just used a hack saw to make it the same length as the old piece I was replacing, and that's about it. There is a little divider inside the pipe that I think will prevent fluids shooting "up" the drain pipe into the sink (sorry no pic but you'll see it if you hold one). Also, my washing machine drains INTO the sink, so this drain gets flushed every now and then (not sure if that really matters or not). You'll see that I extended the hoses with the heavier duty vinyl hose, which fit right onto the barb. If you are using the stock waste line from the Cat Genie (not extending the hose), I'm not sure if the barb will accept the end of the stock hose, you may need to make a coupler to a section of vinyl hose similar to my coupler, not sure:


Here it is after the install, don't forget your hose clamps!:

To extend the pressurized line, this is pretty easy. You just need a brass coupler, careful some couplers have tapered ends and won't seal correctly, you have to buy the one that is for "garden hoses" that are not tapered. Then just teflon tape and a wrench (I had to use 2 washing machine line extensions to get the 10+ feet):


Extending the waste hose takes a little more effort. The end of the waste hose wouldn't fit inside the heavier duty braided vinyl hose I wanted to use (the clear one with white braiding on the left of the 2nd picture below), so I used a vinyl 1/2" male/male coupler and used a short length of standard vinyl hose. In retrospect, I could have just used standard vinyl hose all the way from the waste hose to the nipple on the drain pipe, not sure why I didn't, perhaps the vinyl hose wasn't rigid enough, I did this a month or two ago just getting around posting these photos though (I know the coupler picture says 3/4 but trust me its 1/2" I took the photos just last week not when I did the install month or two ago).


Regarding extending hoses: obviously the pressurized line there is not much to worry about. But, the waste line has to be hung correctly so that the sludge doesn't have too far "up" to travel for the pump, you don't want too much "head" on the pump its probably not that strong and might tax the motor or result in improper disposal. On my install, I have the stock waste line coiled around 1.5 times under the unit, then out the back and up to the "electrical plate" hole, which is the same height as the other electrical outlets. Then, inside the utility room, I have the hose going at a 45 degree angle or so up to 4 feet max height, hang it over a nail/holder/hook/etc, then it slopes downhill about 5 feet to the drain (I have the coupler on the way "up"). So, in the end I have the "flat" part of the line at first(coiled under the unit) as indicated in a normal setup (shouldn't go immediately upwards), then sloping up to about 4', fairly similar to a normal install. The downhill slope after that should matter much, you just can't expect the pump to produce enough "head" to push the waste 10' up. Been running for a good while now, seems to be working ok. If you have not actually seen one of these units work yet, you won't understand that this flushes a ton of water out the waste line during its cleaning cycles, I'm not worried about sludge in the longer line back-flowing into the unit.
Also, since the CatGenie sits in a different room, to cross through the wall, I drilled out two small holes only large enough (about same spacing as an electrical outlet if you know what I mean...) for the hoses to squeeze through, then cheated and put a square light switch plate cover over the holes (there's no electrical box on the other side but I suppose you could get fancy if you wanted to). Just screwed the plate into the wall, and I used two big rubber washers around the hose to cover up the holes in the wall and make it look spiffy (put the rubber washers on the hose before you connect the lines to the drain!!
Remember, I'm not an expert, and if you are a lawyer, use at your own risk


