Can't Apply an Artifact Appearance

To apply a Legion artifact appearance to a regular weapon, visit any transmogrifier. 

Collection Filters

If the transmogrifier doesn't show the appearance you want to apply, check your filters and your current talent specialization. 

Selecting Legion Artifacts will show you only the artifact appearances for your current talent specialization. For example, if you are a Druid in Guardian spec wielding a staff, the drop-down will show you the Claws of Ursoc appearance, and not the Scythe of Elune appearance as this is a Balance spec artifact. You can apply Claws of Ursoc to your staff (because artifact appearances ignore general restrictions as explained above). You can also apply the Scythe of Elune appearance to your staff, but to do this you will need to select the Staves drop-down, not the Legion Artifacts drop-down.

Selecting any drop-down other than the Legion Artifacts drop-down will show you the appearances that can be applied to your currently equipped weapon. Following the Druid example, if you are a feral Druid wielding a staff, you can transmog your staff to Scythe of Elune using this drop-down. 

Druid Customization

Applying the Legion artifact appearance on a weapon at the transmogrifier has no effect on your cat or bear form. Druid shapeshift forms can be selected at the Barber Shop.

If you are unable to change to your druid's artifact appearance at the Barber Shop, make sure you don't have any glyphs equipped.

Account-wide but Class-specific

Appearances are account-wide, but artifact appearances are class specific. For example, if you are a Warrior, you can apply any artifact appearance that you unlocked on any Warrior on your account, but not artifact appearances you unlocked on a different class such as a Death Knight. If you have the Apocalypse on a Death Knight, this is a sword, and Warriors use swords; however, a Warrior won't see that appearance available at the transmogrifier.