LWJGL’s source comes with a nice space invaders demo, always a nice place to start.
you can get it either by downloading the lwjgl source code package or you can grab/view it from lwjgl’s svn http://java-game-lib.svn.sourceforge.net/viewvc/java-game-lib/trunk/LWJGL/src/java/org/lwjgl/examples/spaceinvaders/
theres also the demo’s page over at http://www.lwjgl.org/demos.php which includes demos and source for some basic stuff.
also try the irc channel at #lwjgl on freenode.net, very helpful ppl over there, they can usually help and solve any issues you may run into.
as for binaries, LWJGL comes with precompiled binaries for all the major platforms so you really only need to worry about java code and just include them with your game.