In a kitchen remodel, I am installing the dishwasher about 3 feet from the sink. How do I plumb it?

https://www.homedepot.com/c/ah/how-to-install-a-two-handle-kitchen-faucet/

http://www.planitdiy.com/how-to/plumbing/how-to-replace-a-kitchen-faucet/

The new faucet should come with instructions as well

I have because I want to protect my good dishes from getting cracked or me dropping them and having them break. Its also to protect the sink from getting scratches from the dishes.

i thought I responded to this.

make sure the air gap in the kitchen plumbing (if installed is clear). Also check the kitchen drain is not blocked. If using garbage disposer in sink, then make sure it is run before you start the dishwasher.

if you have an air gap vent in the kitchen sink plumbing then make sure it is clear. Also looks like the kitchen drain end is blocked. Pour some caustic soda into the sink drain, wait 10 minutes and run water into the sink.

If you are using insinkerator (garbage disposer) in sink, make sure it is run before you start the dishwasher.

For water supply, use a braided stainless steel flexible dishwasher supply hose with 3/8 compression ends on each side and a 3/8 male NPT x 3/8 compression elbow adapter. There is a tee with 3/8 female compression x 3/8 male compression x 3/8 male compression which can be used between the hot water shut off valve and the supply tube to the kitchen sink faucet to get your hot water with no significant plumbing work. Make sure the drain hose does not run straignt down back to the dishwasher. (put a loop up to make sure no dirty water tries to go back to the dishwasher.) If installing drain to a disposer drain port, make sure the knock out plug has been removed. It's also easiest if the floor under the dishwasher is at the same hight as the rest of the floor in the kitchen. Make sure wire nut connections are tight for electrical.

Its normal to have the water supply from under sink to dishwasher 3/8 soft copper. If there is a water stop under sink for dishwasher go ahead and shut it off. If not you will have to shut water off at main. Now you can unscrew supply at dishwasher, it's close to the front on left side. Its a 3/8 compression nut, you can use a small cresent wrench.

OK, I have made this error before.
When you install a new garbage disposal, it comes with a "plug" that fills the hole of the little pipe that the dishwasher drain hose connects to (if there is a dishwasher.)
Remove that plug (see instructions for the disposal) and you should be all set.
Also, if you ever get the chance, consider installing a dishwasher AirGap valve between your dishwasher and garbage disposal. They are almost free at any hardware store.
Good Luck! Please report back with what you find.

You can remove the feet from the bottom of the dishwasher

To get the water to the dishwasher, it depends on your plumbing setup. If you have shutoffs under your sink(1/2" X 3/8" compression angle stop), you will need to buy a 1/2" x 3/8" compression double stop. This will be easy to change.

#1 Drill a 1 1/2" hole in the back bottom of the cabinet to run your water, drain line, and power cord through.
#2 First turn off the water at the Hot Water Tank, or the House supply, and turn on the sink to relieve the pressure.
#3 Next remove the Hot supply stop, and install the double stop.( The nut and ferrul do not have to be removed, as they will attach to the double stop. Reinstall the hot supply to the sink to one of the connections on the double stop.
#4 Install a 3/8" x 3/8" x 48" braided flex with the 1/2" MIP
x 3/8" compression ell at the dishwasher.
#5 Install the drain hose supplied with your dishwasher at the bottom of the dishwasher.
#6 Install a 6' pigtail power cord to the power box under your dishwasher.
#7 Feed the drain line, power cord and water supply through the hole in the back of the cabinet at the bottom. As you push the dishwasher back into the enclosure, you will need to feed the 3 lines into the cabinet under the sink.
#8 Attach the water line to the open connection on the double stop.
#9 The drain line will attach to your garbage disposal.(If you have one) Be sure to knock the small piece of plastic out of the drain connection, and retrieve it out of the disposal, before connecting the dishwasher drain line.
#11 Raise the middle of the drain line as high as possible under the cabinet under the sink, preferably attach it to a screw to the bottom of the counter top. This will keep the dishwasher from drawing a back siphonage and getting a bad odor.
#12 Plug in the dishwasher. Assuming you have electrical under your sink. Otherwise an electrical outlet may need to be installed.
#13 Balance the dishwasher using the front legs. After you adjust the depth of the dishwasher, and the level. Use the 2 mounting screws included with the dishwasher to fasten the 2 clips above the door to the bottom of the counter top.
#14 Remove the installation manual and styrofoam from the tray, and turn the dishwasher on. Inspect for leaks as you run a cycle.
#15 Attach the bottom kick panels

You are done.

If you have any questions, please let me know.

Dbootin,

I suggest just putting a dedicated Drain in the island next to the Dishwasher. You can hide it in side the island. Under the house, tee into the Main Sewage drain.  You should not need to vent it as the sinks vent is near enough to keep you from worrying about that.