Most of these methods should work fine on vWii.
This is a guide on how to connect to Wiimmfi.
There are multiple methods on doing this so I'll cover those. If I don't list your method, DM me it and I'll add it to here.

1. Built In
Let's start off something basic.
If your game of choice has a modern/updated modpack for it. It may have Wiimmfi support.
EX: Project M (Wi-Fi Set), Custom Track Grand Prix Revolution, Brawl Minus, etc.

2. Gecko Codes
Certain games like Super Smash Bros. Brawl have a code that allows you to connect to Wiimmfi instead of WFC.
This is also very easy, especially if you already know how to make a GCT.
If you don't though, here's how to.
S1: Go and download codemanager.exe
S2: Open it and set the game ID to your game's ID and hit "store name/id". The first 3 letters are the main ID, so EX: RUU = Animal Crossing City Folk. The 4th letter means your region [E= NTSC-U, J= NTSC-J, P: PAL]. Then put 01 next to the 4 letters. Name of the GCT doesn't matter.
S3: Hit "Add a code/comment/category" and type the name of your code then hit "OK".
S4: Select your new code and on the right side, type your code of choice. I have in the spoiler section the Wiimmfi Patch code for SSBB.

Spoiler

Wiimmfi Patch:
0648EE00 00000010
7769696D 6D66692E
64650000 00000000
0648F808 00000010
7769696D 6D66692E
64650000 00000000
06489F64 00000014
2E776969 6D6D6669
2E646500 00000000
00000000 00000000
06489F84 00000014
732E7769 696D6D66
692E6465 00000000
00000000 00000000
06489FA8 0000000A
7769696D 6D66692E
64650000 00000000
06489FC8 00000014
732E7769 696D6D66
642E6465 00000000
00000000 00000000
06489FE8 00000014
732E7769 696D6D66
692E6465 00000000
00000000 00000000
0648A008 00000014
732E7769 696D6D66
692E6465 00000000
00000000 00000000
0648A028 00000014
2E776969 6D6D6669
2E646500 00000000
00000000 00000000
0648A04C 0000000A
7769696D 6D66692E
64650000 00000000
0648A070 00000030
2E776969 6D6D6669
2E646500 00000000
00000000 25732E6D
7325642E 67732E77
69696D6D 66692E64
65000000 00000000
0648D41C 00000070
3A2F2F6E 61732E74
6573742E 7769696D
6D66692E 64652F61
63000000 00000000
00000000 68747470
3A2F2F6E 61732E77
69696D6D 66692E64
652F6163 00000000
00000000 00000000
68747470 3A2F2F6E
61732E64 65762E77
69696D6D 66692E64
652F6163 00000000
00000000 00000000
0648D49C 00000070
3A2F2F6E 61732E74
6573742E 7769696D
6D66692E 64652F70
72000000 00000000
00000000 68747470
3A2F2F6E 61732E77
69696D6D 66692E64
652F7072 00000000
00000000 00000000
68747470 3A2F2F6E
61732E64 65762E77
69696D6D 66692E64
652F7072 00000000
00000000 00000000
0648DD30 00000014
2E776969 6D6D6669
2E64652F 00000000
00000000 00000000
0648E880 00000010
7769696D 6D66692E
64650000 00000000
0648EE00 00000010
7769696D 6D66692E
64650000 00000000
0648F808 00000010
7769696D 6D66692E
64650000 00000000
0648FF80 00000014
2E776969 6D6D6669
2E646500 00000000
00000000 00000000
064909DC 00000014
2E776969 6D6D6669
2E646500 00000000
00000000 00000000
06490C00 00000014
67732E77 69696D6D
66692E64 65000000
00000000 00000000
06490C1C 00000014
67732E77 69696D6D
66692E64 65000000
00000000 00000000
06490C38 00000014
67732E77 69696D6D
66692E64 65000000
00000000 00000000
06490D88 00000014
67732E77 69696D6D
66692E64 65000000
00000000 00000000
06490FB8 00000014
732E7769 696D6D66
692E6465 00000000
00000053 00000000
0648DE08 00000010
3A2F2F2F 646F776E
6C6F6164 00000000
0648DE58 00000010
3A2F2F25 732F646F
776E6C6F 61640000
044905EC 3A2F2F00
044905FC 3A2F2F00
044908D4 3A2F2F00
0449164C 3A2F2F00
04492414 3A2F2F00
Made by: Diddy Kong and Doqtor Kirby

S5: Once you're done putting the code in. Hit "Export to GCT" at the bottom. Hit "Yes" and export it to your PC's drive.
S6: Now put your new GCT in sd:/codes/ and launch the game in Gecko OS with SD Cheats set to ON.

3. ISO Patcher
You can skip this method if you're using a USB Loader that has a 'Private Server" option.
You only need to do this if your Wii's disc reader broke.
You will need an ISO of the game you wanna patch and the ISO patcher for your game.
There are different ones, one for MKW, one for ACCF, and one for all other ISO dumped games. (This will be focusing on the MKW and Other Games patcher since the ACCF one works differently.)
S1: Download the patcher and extract the 7z.
S2: Open the extracted folder and go to the OS folder that is for your OS. (EX: Windows)
S3: Now drag and drop your game ISO onto the wiimmfi-patch file (Dot bat is you are using Windows, dot sh if you are using OS X/Linux.)
S4. Now just convert your ISO to a WBFS and put it onto your USB and from there load it.

4. Disc Patcher
This is for playing games that don't have a modpack that comes with Wiimmfi support.
S1: Download the Disc Patcher and put it on your SD card.
S2: Run the patcher in HBC and then insert your game disc if you haven't already.
S3: Wait a bit then the game will launch. You should be able to connect to Wiimmfi if successful.

5. Flashhax
Same reason as above but you don't want to mod your Wii.
S1: Go onto the Internet Channel, if you haven't downloaded it yet, get it from the Wii Shop Channel.
S2: Go to chadsoft.co.uk/wiimmfi/.
S3: Go to your Favorites menu and add the site as a favorite, now reboot Internet Channel.
S4: Go to Favorites and select the favorite you just created, now insert your disc if you haven't already.
S5: Same as S3 of Method.

And that's it. I hope you guys can finally play Wiimmfi now. Here's a few notes to give though.
1: If you try to play Mario Kart Wii on Wiimmfi on a new console, it will give you 23899. Just simply wait a week after getting 23899. If you try to connect in MKW before a week as passed. You will get other 238XX errors. Check wiimmfi.de/error to see how much longer you have to wait. For other games however, this doesn't happen.
2: The ISO Patcher method is also needed for Wiimmfi on Dolphin.
3: If you haven't used your Wii in a while and try to connect to Wiimmfi, you may get Error 60000. That means that your save has a WFC friend code that's not in Wiimmfi. The usual way to fix it is to delete your save or at least profile. In Mario Kart Wii's case, there's a code that removes the PID from the license without removing anything else from it. http://wiki.tockdom.com/wiki/Clear_Profile_ID

 

[banjo2]

Very nice and short, though no mention of error code 60000...?

 

[GreyWolf]

Using USB Loader GX at least only requires the loader. It has built-in Wiimmfi patching.

 

[FancyNintendoGamer567]

@banjo2 If you get Error 60000, that means your save has a Nintendo WFC (old servers) FC, in order to connect to Wiimmfi. You may need to delete your save.

 

[banjo2]

@banjo2 If you get Error 60000, that means your save has a Nintendo WFC (old servers) FC, in order to connect to Wiimmfi. You may need to delete your save.

Yes, I know, but that isn't mentioned in the tutorial. Also, 60000 can be solved on MKW without deleting your profile with a special cheat code.

 

[FancyNintendoGamer567]

@banjo2
I guess I'll add that then, also I already knew that.

 

[FancyNintendoGamer567]

It seems that WiiFlow Lite also allows you to patch Wiimmfi onto a game on the loader itself.

 

[FancyNintendoGamer567]

Decided to bump this in case someone needs this.

 

[fst312]

Quick question I never used cheat codes on the wii and I’m wondering in your spoiler for smash bros will that cheat code fix the error 60000 for the game or am I stuck deleting my save file. Since I recalled Mario kart having a cheat file to go online awhile back, I’m wondering if that smash bros cheat code does the same thing.
I know it may not because I did read that part in your post but I’m also wondering if a cheat code was ever made for this.

 

[GamingJam]

Priiloader also let's you patch through the disc channel! This is pretty nice, came out somewhere in 2020.

 

[FancyNintendoGamer567]

Yeah, I know that. I should probably get Priiloader 0.9 now.
BTW, if you don't know how to use it, just enable the Wiimmfi Patch hack that's somewhere on the hacks menu.
@GamingJam