How are the big programs made

[Mats]

The UE3 engine has tens of thousands of lines of code(if not, hundreds of thousands) . I can only assume UE4 has more.

According to the link OrionMaster posted, it has around two million.

[BlakeK]

Yeah you could buy UE3/4. But why don't you just get involved in an open source project? I've involved in Linux Mint. I've heard a lot of coders seem to like LibreOffice. Both these projects are fairly large, have every aspect of code, and have incredibly friendly/helpful communities. I mean you learn about revision control systems, bug tracking, coding style, artwork involvement, the list goes on. I recommend you check out a medium-sized code base using git and just play around with it. I mean the only cost to you is your time, so why not?