Andreas.d I'm a newbie to all this and I can tell you what I did and it was fairly painless in the end. I downloaded RealVNC Server onto my Pi3. You can go to their web site to get the Raspberry Pi download version. I just walked through the setup screens and got it running. Port forwarding wasn't as mysterious as I suspected. I used info on a web page
www.portforward.com that helped me do it with no snags and while I was in the router settings I made the IP static for my Pi3 (I also made the IP static within the Pi3's Internet connections settings to match it all so I can connect the Ethernet cable directly from the Pi3 to my Laptop if I want). The port is 5900 for RealVNC Server. Locally, I added RealVNC Viewer (downloaded from the RealVNC web page) to my laptop (they'll ask you to register it for free) and I'm able to remote into my Pi3 both via Ethernet or Wifi over my LAN just fine; you just need to have the IP address for the Pi3 on your router.
I just had RealVNC configure my Pi3 user name and password as the login, but the viewer will allow you to click a menu item and allow "Guest Access" temporarily. That's what I did for Jasem and he got in without needing a password. Yeah, not exactly super secure, but my Pi3 doesn't have anything on it that I'm worried about.
The RealVNC web site somewhere is where I got the terminal command lines to start and stop the VNC server and I created launchers on my desktop to do that real quick without having to remember the commands. I ended up setting the VNC startup launcher to automatically run at startup for me so I don't have do it each time.
Of course, there are other VNC server programs out there to use, this is just what I ended up using and without knowing what I was doing I managed to make it work.
I googled, "What's my IP address" and found numerous web pages that will ping your IP address and tell you what it is; so when you go to have someone connect from outside, you can tell them that IP address.