Dark Age Computing
The first stumbling block that many people encounter with LilyPond is text input, no GUI (graphical user interface). It's too bad that this one fact would drive so many people away. Just because it doesn't have shiny buttons or drag-and-drop shouldn't make you give up on something great! It's time to loose yourself from the shackles of GUIs and embrace the stark beauty that is text.
Your First Step to Freedom
Remember, if you're going to learn something, you just have to dive in and do it! If you're just starting to learn Lilypond, look through the introductory notes in the documentation. It's not like you're taking a test on the material, so don't try to memorize all this. Just try to familiarize yourself with the input and general development flow.
After you see the introduction to LilyPond, download some files and typeset them. There's sample files all through the documentation, or you can just download my files and try them yourself. Once you have some files, try modifying them to transcribe your own files. As you practice, you'll learn what the commands mean and which ones you need.
I Want to Do X in LilyPond, But I Don't Know How
The documentation is not particularly easy to navigate, so you use plan B: google it (which is actually plan A for most of my life). The all-knowing google will tell you whatever you want to know. Just type in "lilypond grace note" or "lilypond pickup" or "lilypond medieval style" or whatever you want to know and you'll be on your way.
So grab a few LilyPond files, start transcribing some music, and enjoy the freedom of text!