HELP! Dolphin's Traversal Server is down and I must get my SMASH on!

FEAR NOT! There is a way!

Step 1: Port Forwarding Your Router

When it comes to port forwarding, most routers are completely different. We recommend using Portforward.com's Guide List in finding your router and designating a specific port for access within dolphin (The most common port is 2626). In regards to UDP or TCP, if you can select both, then do so, otherwise, go for UDP.  Make sure you APPLY/SAVE your setting. This is a VERY common error.

Step 2: Finding your IP Address

In order for you to have others connect, you will need to locate your External IP Address.

Click here to find your external Ip Address 

You can also type "What's my Ip address" into google and it'll display your ip address.

This is the the ip address you'll give to the person that's going to connect to you. 

Notice that it's different from the address used in step 1!

Step 3: Hosting

As the host, you will need to provide your External IP Address AND the port you forwarded. This info, you need to have written down as you will be giving it to the user connecting. 

Within the Dolphin Netplay Setup window in the top left, make sure you click on and select Direct: 

Click on the Host tab and specify which port you successfully port forwarded (make sure you saved your port forwarding settings) and click host:

From this point, you will need to provide your External IP Address and the Forwarded Port to the person you wish to connect with. As the Host, you're done!

Step 4: Connecting (I want to connect to a person that forwarded their port!)

You will be given the External IP Address and the Forwarded Port. From here you will open up the Dolphin Neplay Setup Window and click on Direct as well. From here you will input the IP address they gave you and the specified port they forwarded and hit connect:

And there you have it! You're connected again! 

Oh Nos! Security!!!

Anther Amendment - 
There are NO security implications to port forwarding over using the traversal server.
In super basic terms, I'll break it down a little bit.

With The Traversal Server

1 - I HOST

2 - Traversal server stores your IP address and gives you an 8 digit code that you share

3 - Other Person gives traversal server the 8 digit code, traversal server sends them your IP Address, which then uses the magic of the internet to communicate with you

Without The Traversal Server

1 - I HOST

2 - No Traversal Server, you just share your IP address

3-  Other Person puts your IP address into dolphin and uses the magic of the internet to communicate with you

CONCERN 1)  OH NO SOMEONE HAS MY IP

Without using the traversal server there is no code to exchange. That's the BIGGEST DIFFERENCE, so basically this means your argument is that you're claiming that a person that is not technical enough to get your IP address after getting a host code from the traversal server, is now more dangerous to you than a person that could have done this with a TINY bit of technical knowledge.
At worst ignorant people can try to scare you but now that you have knowledge of how this all works, you can say YOU DON'T SCARE ME BOOGEYMAN.

CONCERN 2)  BUT THE PORT IS FORWARDED

Here's how this works, typically if you type someone's IP address into dolphin and a port number like 2626, the message makes it all the way to their router, but the router says, "Uhhh, what do I do this this?" And ignores it.

If you port forward the router knows what computer probably wants that data, so it sends it to the PC you told it to send the data to.   Windows checks to see if you have software waiting for messages on that port, like dolphin, and then YAY we play video games!!

The next thing people say is, "BUT WHAT IF THE PC IS COMPROMISED".   If the pc is compromised port forwarding is not going to be what did you in. 

CONCERN 3) BUT DDOS?

Like I said in concern 2 and concern 1, your IP address is already shared, and the message always makes it to your router. DDos (which is illegal for someone to do to you) is a result of someone sending so many messages to your router that its CPU can't handle it.  Idk what else to say here.  You're being paranoid, stop it >:(.