Hi, the easiest electrically controlled valve to find is one from a clothes washing machine or possibly a dishwasher. Those are driven by 120VAC (USA) or 220VAC (Europe, China etc).. These valves take a regular hose connection in (use a washing machine hose). They usually have a smaller hose output connection.. 1/2" to 3/8" you can adapt stuff.
For controlling these valves, and power in general from Arduino see the http://ArduinoInfo.Info WIKI here:
You have to be willing to connect (or get electrical help in connecting) 120V AC wiring to the valve. A good way to connect to Arduino is with a prebuilt relay board like these:
You can get these from my (self-serving) shop or on Ebay from many suppliers.
Setting a small time ON every so many hours can be done with regular Arduino timing. The exact time may drift a little over many days, but the plants won't care. If you want to control by day / hour / minute you will need a "real time clock" like one of these:
Another possibility is to use a windshield washer pump from a car, which runs on 12V DC. Lower voltage and not the concern with properly covering all the wiring connections like 120V AC.
DISCLAIMER: Mentioned stuff from my own shop...