Under sink - Keeping in mind that I am a hack plumber (some of the other guys are probably better at this than I, Worth definitely is)
Your under sink setup does look like the one in the video, right?
I would try to stay away from the need for the compression fittings.
1. Break the existing water line as in the vid, insert tee, with the 2nd nipple coming out of the branch.
2. Get a 1/2 in to 1/2 in hose connector and connect to the branch.
http://www.lowes.com/pd_100999-104-L...nes&facetInfo=
3. Insert a
- Watts A-663 Brass Garden Hose Adapter, 3/4-Inch x 1/2-Inch MPT, into the connector.
http://www.amazon.com/Watts-A-663-Garden-Adapter-4-Inch/dp/B004VT3S4G
(didn't see it on the lowes site)
4. Attach the garden hose shut off valve of your choice to the adapter.
5. Attach garden hose.
6. Water Plants.
7. Eat tomatoes.
You could forgo the 30 in supply line and just insert the garden hose adapter directly into the tee, but I would put the line in so I could have the shut off right inside the door as opposed to having to reach way to the back every time.
And don't forget to get a roll of the white thread tape and use it on every connection, including the hose connections.
Edit - for number 4 - use something like this as this line will be under pressure.
http://www.lowes.com/ProductDisplay?...llow&cId=PDIO1