Applying loose eyeshadow is basically the same as solid eyeshadow.
You can either use brush or sponge tip to apply and for best result use mixing medium or base.
Check out the recipe for mixing medium here
To apply using mixing medium :
Damp your brush (make sure it is not too wet, use tissue to remove the excess) with mixing medium and pick the loose shadow, make sure to tap before put the shadow in your eyelid.
Another way is to make a shadow paste, put small amount of mixing medium in small container put small amount of loose shadow mix it to become a paste.