Download speeds will be slow due to limitations in the network hardware of the Wii, but it remains a valid solution if you are willing to be patient.
Your Wii and your computer must be connected to the same local network.
Downloading
Extract DVD Dump Tool and put it in your apps folder on your SD card or USB drive
The root of your SD Card should now look like this
(root)
apps
DVDDumpTool
boot.dol
icon.png
meta.xml
Insert your SD card or USB drive into your Wii and launch DVD Dump Tool from the Homebrew Channel.
Usage
Press D-PAD Right, then press A
Select the proper disk type for your game, the options are: GameCube Disc, Wii Single-Layer Disc, and Wii Dual-Layer Disc
If you are dumping one of the 13 games on this list, select Wii Dual-Layer Disc
Insert the disk you want to dump
If it is already inserted, eject and reinsert the disk
Press any button to start the dumping process
Remember or write down your Wii’s URL (IP address)
On your PC, open your web browser, go to the address bar, and enter your Wii URL
Click on Click here to download XXXX.iso, once it's done, go to joining PART files
Joining PART files
If you dumped the disc (regardless if it was to a PC or Wii) on a FAT32 formatted device, you should have gotten at least two files that end with .partX.iso. They need to be joined.
Copy the files with the same name and end with .partX.iso into a new folder on your computer
In this folder, click the address bar in Windows Explorer and type cmd
Type copy /b *.part?.iso game.iso, then press enter
Wait until the merging process finishes, It should end with it outputting 1 file(s) copied
Copy the files with the same name and end with .partX.iso into a new folder on your computer
Open the terminal
Run cd [PATH], replacing [PATH] with the folder path to your .partX.iso files
Use the following command as is: cat \*.part?.iso > game.iso
Wait until the merging process finishes.
You have successfully dumped your Wii/GameCube disk!