Well you can basicly just open Wikipedia, search for Internet protocols and start from there, understanding the major layers is pretty much mandatory if you really wanna understand how the network works. There is TCP/IP model and OSI model, the first has four major layers, and the latter has seven layers. If you can understand well what is the "job" of every layer on both models, and you can make basic subnetting (IPv4) calculations and you understand difference between UDP and TCP, you've done pretty good job, and from there I am sure you can keep going on easily.
Also understanding some very basic protocols like DHCP and DNS is pretty darn important. Read stuff about them from the internet, also YouTube has some great videos to explain these and many other basic network-stuff (as someone already mentioned, great example: elithecomputerguy). Just try to use as many sources you can to gather you information, write stuff down for yourself, and when you think you start to understand some concepts, explain them to yourself by writing and making graphs, after that try to check if its correct (this might be hard and there is always risk that you might learn stuff incorrectly when you try to gather information from many different sources, this is why I would recommend to find good and thick book, as written word from trustworthy author is usually pretty... trustworthy).
Learning this stuff by yourself might be very hard and frustrating, but finding a good book which is put together well, would be more than a great start and supports well the information you can gather from internet, sadly I don't know any books (someone here might know some?).
I'm going through the Cisco's CCNA course in university, I have access to Cisco course material, which is pretty much perfect for learning, even without instructor (my opinion), sadly it isn't publicly available to my knowledge.
To summary (try to understand the following concepts):
- TCP/IP and OSI model layers, and what they represent
- IPv4 (subnetting, private addresses, understand the binary form. YouTube is your friend, not a easy concept to understand fully)
- TCP vs. UDP
- Protocols like: DHCP, DNS, FTP, SSH, etc...
- Understand the structure of packets (different datagrams inside the packet, and how they're put together)...
- ...and how packets move inside the network (knowledge about different layers is essential to have at this point, I believe).
On the way you might learn about routing and switching little bit, but after you have the basic knowledge, you can start to investigate that area more in depth and continue to deeper waters. Cisco Packet Tracer is also great simulator, if you can get it, get it. GNS3 is free simulator (I have never used it), but I think you still have to buy the Cisco IOS (or other networking operating system) to run it on the simulated routers/switches. Wireshark is great software to monitor network traffic, packet by packet (nice way to learn about different protocols and how they work, like three-way handshake etc..), but I recommend using it only inside a closed network (no internet access), or you'll never find the stuff you really want to monitor (so basicly making small LAN between few computers). There is many videos on YouTube that help you to understand these softwares.
Lots of information, and sure this ain't the perfect "How to learn basic Network stuff by Yariko", but stuff that I believe is good to know at least. And I am not a professional yet, so someone more experienced can add up, or correct my views on how to get started.
And if you fail at learning this stuff by yourself, don't get disappointed, it's not a easy thing to learn without any guidance or good learning material.