Product review (5 stars): How to connect to pipes under the sink
I use this in a guest unit but if my current full-sized dishwasher unit ever breaks I think I will replace it with this.  It works really well but I have never tried it on anything difficult to clean.

I spent about eight hours at various plumbing and home-improvement stores - trying every single possible connection and asking for help from knowledgeable plumbers - but ultimately it involved picking up every single piece of pipe and tubing in the store and trying to match them together.

Here are the labels on the packets:
One Brass Pipe Tee T  Connector 1/2" FIP
Three Brass Pipe Hex Nipples 1/2" MIP
One Dishwasher Elbow 3/8" OD x 3/4" GH
NPT= national pipe thread = MIP= male iron pipe = FIP=female iron pipe. All use the same threads, at least here in the USA.
GH = garden hose
OD = outside diameter, seems to be what is used on faucet supply lines.

Attach the nipples to the T connector as shown in the picture (I used plumbers thread-seal tape.)

Then you need the connecting faucet supply lines.  The two lines going into the T connect to your hot and cold water lines.  Just buy lines where one end is is 1/2 in MIP/FIP/NPT and the other end attaches to a system that will branch water from your wall outlet (sorry I didn't keep those packets - let me know if you need more details on this and I can check to see what I used.)  The line going into the dishwasher has one end 1/2 in MIP/FIP/NPT and the other end attaches to the dishwasher elbow 3/8in OD.  The other end of the dishwasher elbow attaches to the dishwasher.  (Too much detail probably!)
Then I cut a hole in the drain pipe above the trap and the dishwasher drains directly into the drain.
(sorry that the picture shows the metric version of the sizes - 1 cm is 3/8 in and 1.27 cm is 1/2 in.)

What I have learned since doing this:
Now I also see there is something called a "Y Washing Machine Mixer Hose" which may be useful, since the attachment going into the dishwasher is the same size as washing machine connections.  (I think.)
Also, since the dishwasher has an internal water heater, you could just connect this to the cold water if you just wanted to deal with one supply line.