The traditional way to access MC from outside your local LAN is to open what is called a port on your router. By default MC uses port 52199, although this can be changed in the Media Network - Advanced. Look for TCP Port and it should say 52199. What you need to do is "open" port 52199 on your router and associate it with the ip address of your MC computer.
To find out the ip address of your computer you can go to Control Panel - Network and Sharing - then select your network adapter - then select Change Adapter Settings and then select Details. Under IPv4 will be a number like 192.168.1.10. The 192.168 are pretty standard and the next two numbers (1.10) will be specific to your computer. Alternatively, if know how to get to the RUN command, you can type ipconfig on your MC system and it will show you the ip address, among other things. Tge exact details of how to get the Network and Sharing will depend on what version of windows you have, but you should be able to find it. Here are some instructions.
http://www.digitalcitizen.life/4-ways-learn-your-computer-s-ip-address-windows-7-windows-8
Now, you need to connect to your router and choose Forwarding > Virtual Systems, then add the port number (52199) and the ip address.
Instructions for your router are here
http://www.tp-link.us/faq-72.html
Hope that makes sense. Give it a try.
My routers instructions to open ports on my TP-Link AC1900 Gigabit Router, dual band, (Archer C9) router:
Click Forwarding->Virtual Servers on the left side, and then click Add New… button.
Type the Service port which you want to open and the IP Address of your device that you want to open the port for; Select Protocol to TCP, UDP or ALL; Change Status to Enabled.
SETTINGS:
Service Port: (xx-xx or xx)
Internal Port: (xx, only valid for single service port or leave blank)
IP Address:Protocol: (All, TCP, UDP)
Status: Enabled
Common Service Port: (DNS, FTP, GOPHER, HTTP, NNTP, POP3, PPTP, SMTP, SOCK, TELNET)
SAVE, BACKWhere do I enter the IPv4 address obtained by ipconfig from the run command?
Where do I enter the IP address from
http://www.whatsmyip.org/ ?
Where do I enter 52199?
Which Protocol do I use? (All, TCP, UDP)?
Which Common Service Port do I select? (DNS, FTP, GOPHER, HTTP, NNTP, POP3, PPTP, SMTP, SOCK, TELNET)
TIA