Intro:
My reason for this "Tutorial" is to make you aware that there might be other, safer, alternatives out there. I will try to explain the basics and then I will give you some links where you can further you study, should you choose to do so.
You are welcome to ask questions in here and I will try to answer.

Start: 
I saw alot of you guys asking about how to mod your Wii, buy modchips from secure sites and that stuff.
Given the raids in america, that I have only read about(European here) it seems it would be quite dangerous to order/buy Wiikey and other modchips.
But there is another alternative. Its cheaper. It works just as well for backups. Another good thing is that it will not get the Feds on your neck since you will be buying super common components. 
The catch is of course that it requires some work.

I have done this myself, and for some friends aswell. I know that it works for "old' Wii´s. 
I have read that it is harder to mod the newer versions. Since I have no experience with those, Its hard for me to say how hard.

What you need:

Instead of buying a Wiikey, Cyclowiz, Wiinja or other pre made Wii modchips that are now illegal you can make your own instead.
This might seem hard to you, but it really isnt that hard.
All it takes is the VERY common and well supported 'Atmel Atmega8' microcontroller. Though it is highly recommended to have a capacitor and a socket aswell. 

However, This is assuming the microcontroller is pre programmed. Its not, but you will program it yourself, with one of the many firmwares available on the internet.
To make a simple programmer you will need something like 7 resistors, a socket for the microcontroller and a parallel port plug for the computer.

Besides that you will only need a soldering iron, some thin wire and some soldering tin.

If you have absolutely no experience with soldering you might get a friend to help you. TBH its not that hard if you are patient and carefull.

Links for more information:

http://www.openwii.org/ 
This is the firmware I would recommend you to use, their guides looks fine aswell.

http://chiip.descrambler.de/ 
This hasnt been updated for a long time, but the info about chip, programmer, but I think the guide for building the programmer is better. Besides everything here is for the Atmega8 ONLY, so there should be less confusion. You can always program it using Openwii firmware.

Edit: There seems to be some software out there that uses PIC microcontrollers aswell. If you have experience with using those, IE. for modding PS2 then it should be possible aswell.

To sum up the total hardware needs:

1x Atmel Atmega8 microcontroller
2x 28pin IC socket(the small width one)
7x 220ohm Resistors(the normal small 1/4W ones)
1x ~100nF Capacitor(Not Electrolytic)
1x +~50uF Electrolyic cap

All in all I would guess the components would cost between 5 and 20$, but its a guess since I dont know your shops 

If you are worried about your version of Wii, all I can say is that from what I have read the Wii with serial numbers from:
LEH-1000xxxx to LEH-122xxxx is no problem. Other versions you will have to make sure about.
You can find the serial number outside your wii, on the sticker.

EDIT: I forgot one important feature! To open your Wii you need a small TriWing screwdriver. I suggest you to buy that, cause its a fucking pain in the ass to take apart the wii without it!
You cannot use a normal Bit with triwing since its quite small screws and the holes are too narrow for normal sized bits to get in there.

EDIT: Figured I would add some pics I found from when I did my own. Its not made pretty, the cable is similar to the ata33 cable in a computer, smalles we had at school(and fine). Soldering was done with a normal 50W weller(normal tip), the socket is not a full 28 pin as the Atmega8 is, but it doesnt matter since its only 5 pins. So this is how simple it really is, once you get it apart and have the components...