Switching a Kettle On/Off using a arduino
There's a particular problem here with the kettle that a relay will not solve. Kettles always have their own switch which trips off when they boil. So even if your relay is on, the kettle will not heat up unless this switch is also on. If you took the kettle apart and shorted out the switch, it would not trip off when the boiling point was reached, so this is very dangerous. If you think you can also replace the boiling point sensor and run the logic through your processor, you should think about the fail safe implications of this and consider your house insurance situation.
Depending on the type of switch used in kettle, it might be possible to fill it and switch it on mechanically, waiting for mains to be switched on by the micro. But you could only boil it once before having to mechanically reset the switch. If that works for you, fine, but bear in mind that kettle are not like lamps that you could just switch on and off whenever you like, and interfering with the switch is hazardous.
Most kettles that I have come across do allow the switch to be on even when there is no mains, but most toasters don't allow the basket to be latched in the down position without incoming mains, so you can see this could be a problem.
If you want to control a 110V mains power device, a "power switch tail" is available for markets that use the US-style 110V outlets: powerswitch tail
No, you don't have enough parts to build a circuit to switch on your kettle.
If it really is a basic kettle with no logic or low-voltage controls, then the switch is controlling your house voltage (110V/230V) directly. The practical limit to an Arduino or any microcontroller is about 5V. Additionally, microcontrollers can only handle DC voltages. If you tried to connect your Arduino to the kettle without any additional components, it would probably explode.
I would recommend that you use a relay to switch on and off your kettle. It is relatively easy to find 110V/230V AC rated relays, with current ratings large enough for safe switching. It is a fairly simple circuit to set up; you need a relay, a driver transistor, and a diode for relay coil.