1. LilyPond
If you don’t already have LilyPond, you have to install it separately (at least 2.14).
Go to http://lilypond.org/download.html
Download LilyPond stable version for your platform
Install the package
2. Eclipse
If you don’t already have Eclipse, you have to install it separately (at least 3.7).
Go to http://www.eclipse.org/downloads
Download Eclipse IDE for Java Developers for your platform
Decompress the package
3. Elysium
Elysium is an Eclipse plugin, so install it from within Eclipse.
Start Eclipse
Run Help > Eclipse Marketplace…
Search for Elysium and install it (if a Security Warning appears about unsigned content, just press OK)
4. Create New LilyPond Project
To edit your existing scores, you have to create a new project from them in the Score Library.
Run File > New > Project…
Select LilyPond > LilyPond Project
To import existing sources, uncheck Use default location and Browse for their folder