I have done this very recently and have found that it can be ridiculously simple and (if you are willing to pay a bit more) really easy. People are correct in saying that the chip you should get depends on how old/new your Wii is - THEY ARE NOT ALL THE SAME. There are different versions of the DVD drive hardware that are identified with labels - DMS, D2A, D2B, D2C, D2C2 and the very, very new D2E.
The following site can try and estimate what chipset you have from the serial number of your Wii.
http://wiitracker.nintendo-scene.com/search.php
It's not 100% foolproof - the only way to know for sure is to open up your Wii and have a look at the version printed onto the DVD drive. Once you know what version you have, you can make a decision on which mod-chip to get. The only trick to this is that you need a special "tri-wing" screwdriver to get the thing open!
Chipping is traditionally a difficult task involving soldering - sometimes to tiny contacts (esp. with the newer DVD drives) - and easy to get wrong if you don't know what you're doing. Have a look at this:
http://www.wii-clip.com/images/d2pro_13-15-19.jpg
Each one of the labelled points is somewhere you'd have to potentially solder wires to. Not fun. However help is at hand. Some clever people have started making clips that go over the main chip on the DVD drive meaning that the only soldering you have to do is relatively simple.
You go from this:
http://www.wii-clip.com/images/D2pro_V4-02.jpg
To this:
http://www.wii-clip.com/images/D2pro_V4-03.jpg
Then to actually install the thing, you open up the Wii and find the right chip:
http://www.wii-clip.com/images/D2pro_V4-11.jpg
And just clip the mod-chip and it's holder into place (being sure to be firm).
http://www.wii-clip.com/images/D2pro_V4-06.jpg
Depending on the mod-chip and the version of the DVD drive in your Wii, you may need to only connect up certain points from the mod-chip to the clip. This can be a bit confusing. To make even this bit easy as pie, there are plenty of sites online that will solder the chip to the clip for you and make sure they connect up the right bits, provided you give them the right info on the version of your Wii. Then all you have to do is put open up the Wii, put the clip in place, close it back up again and Bob's your uncle.
The example chip I showed above requires extra soldering if you want to enable region free play. There are other options.
The D2Pro9 works flawlessly with only the wii clip and no extra soldering (I ordered this pre-soldered to the clip - installation took about 15 minutes!) and the Wasabi chip has already been confirmed to work with the new D2E version Wii. There's a lot of info out there to look at, but there are plenty of forums much better suited to helping you choose than this one.
Wow. That went on for a bit.
Hope it helps!