I've been quite used to working on small projects which I coded with 1,000 lines or less (pong, tetris, simple 3d games, etc). However as my abilities in programming are increasing, my organization isn't. I seem to be making everything dependent on one one another, so it's very hard for me to change the implementation of something.
Any ideas for keeping my code organized and being able to tackle large projects?
Sketch out an architectural design ahead of time. It doesn't have to be too detailed, but imagine how you want things to fit together in general terms.
Use of design patterns is a good first step.
Also, spend a little time writing good documentation regarding system architecture and requirements for the application.
Using source control will help if you are not already doing this.
Look for libraries that may do want you want before you decide to roll your own.
whiteboards are your best friends
prototype designs (not necessarily working prototypes, use notecards or other methods)
plan first! dont code until you know your requirements/goals
Read into refactoring first (made famous by Martin Fowler).
By learning refactoring, you can learn how to write code which is easy to change, readable, and simplified.
I would suggest not to learn design patterns until you understand refactoring first. With refactoring, you can understand the themes of clean and readable code. Once you understand refactoring, read on to design patterns. Design patterns is very useful when you need to write more complex designs.