so what you need to do is open up a few ports on your router, assuming you are an adult, or have an adult who pays for internet service. If you're on a public network forget it, out of luck.
This should take all of about 3 minutes. I swear it will take you longer to read this than to actually set everything up. Here is what I would do:
Login to the Rpi. run
ifconfig, note your local ipv4 address and your default gateway address, they are most likely in the form 192.168.X.X or 10.1.X.X however it does not matter what format the address is in.
Navigate to the default gateway address in a browser window, you can do this from any computer on your network. Find the section for port forwarding, sometimes it's called application forwarding. It helps to know the make/model of your router (located on the sticker on the bottom) then you can look up a quick youtube to walk you through the process.
Once you find where to do the port forwarding, simply forward the ports you want access to, and which computer you want those ports pointing at.
Let's say your Rpi is located at 192.168.0.14 and you wanted http access in order to view a web site you are self hosting. You would simply forward port 80 to 192.168.0.14 and that's it. Now when you type your external ip address into the browser, from another network, it won't work if you're already there, it will redirect you straight to the web page hosted on the Rpi.
However, you may not know your external ip address, and it may change from time to time, unless you pay for a static ip address from you isp. Don't do that. You don't need it. DDNS is the solution (this is what RalfB is talking about when he said to 'get a URL mapping service'. DDNS stands for dynamic domain naming service. What it does in simple terms: give your external ip address a human readable format in the form of a subdomain like
deenski.issodamnhelpful.thanksdeenski instead of 74.123.xxx.x or something. The DDNS client you will need to install also checks your ip address in 5 - 10 minute intervals to see if they need to 'point' the domain name to a different ip address if yours were to change. I use no-ip for my DDNS provider. However, any of the service providers would be fine. Just search 'free ddns' and you'll find what you need. Typically the providers allow about 3 free hostnames. Note that you do not need to install their updater client on your Rpi, you may use it on any pc on your network, since it is updating the external ip address of your entire network. If you have a machine you leave on 24/7, install it on that one. Once you have it up and running, you should be able to go to whatever.yourchosenhostnameis.whocares and see your working web page.
One more thing though, and if you're ssh-ing into your Rpi, I am sure you already know this, but you won't want to forward port 80, you will want an abstract port number. Once you choose a port you will need to navigate to that port using
whatever.yourchosenhostnameis.whocares:<port number>. For ssh access this would be
whatever.yourchosenhostnameis.whocares:22 (DO NOT PORT FORWARD 22 WITHOUT USING ENCRYPTION KEYS). Sorry for breaking it down to the base level if it wasn't necessarry. Just trying to help.
If you need, here is an article from someone I am sure writes more clearly concise than I do: http://www.groovypost.com/howto/port-forwarding-guide/