you need to look how to open ports for your router and then just open the given ports on Andrews reply or get the same port numbers from playstations site.
it goes like this:
you need to set up a static IP address for your VITA, if you dont, opening ports for the IP address your vita is set to at the time, would be pointless if its dynamic. Dynamic means that the IP address changes to what ever is open, so depending on if a computer or other handheld device takes over that IP, your Vita's IP would change because it'll go to the first IP free when its dynamic. Static IP addresses always stay the same. so your IP address my dynamically be 192.168.1.3 now, but next time you turn on your vita it might reassign to 192.168.1.5 making any ports open to the original IP not work on the new IP.
For instance my Vita's IP is: 192.168.2.44, i set the 44 because most likely any smartphone or computer that connects to my router will use one of the first open ip address like anything between 2-43 so its very unlikely ill turn on my vita and some other device will have taken its address which will cause a connection problem.
once you have a Static IP you open the ports for that IP through your routers admin page. For my router you put in the URL 192.168.2.1 in a web browser. Most routers are just 192.168.1.1 instead. If your not sure refer to your manufactures resourses or on a winds go to Run>cmd and at the command prompt just put in the command: ipconfig/all (this will list IP,default gateway,ect,ect which is also needed to set up an IP address.
for my Belkin Router once I am signed into my admin page, I go to a page called Virtual Servers, although its usually called Port Forwarding or something else on other routers I've had.
i put in the values for each port I'm opening and associate it to the static IP of my Vita. its pretty straight forward actually.
Name-Inbound port-TCP/UDP-IP ADDRESS
PSVITA1 - 80 - TCP-192.168.2.44
PSVITA2 - 3478 - BOTH - 192.168.2.44