If used during the Day, your options are:
Deputy - Announce a Deputy shooting a player. This will fail if the target has Basic or higher defense, but bypasses Ethereal Defense. This cannot be done if a real Deputy shot that day. A real Deputy cannot shoot if this is used and hits.
Prosecutor - Announce a Prosecution on a player. Same rules as Deputy (has defense checks unlike real Prosecutor), and can't be used if a Prosecution has already happened/real Prosecutor cannot Prosecute if you use this and hit.
Conjurer - Announce a Conjure on a player. This is identical to a real Conjure (Powerful Attack, can't hit Ethereal, reveals defense), and can't be used if a real Conjurer went that day/real Conjurer cannot conjure if you use this.
Executioner - Announce Torment today. If a Town member is hanged, you anonymously Torment without leaving the town. If nobody or a non-Town member is hanged, lose your Announce charge anyways. The charge is refunded if a real Executioner torments that day.
Judge - Announce Court today. The real Judge appears as Jury, and you appear as the Court. Cannot be used during a real Court, and Judge cannot call real Court during your Court.
Mayor - Announce your Reveal, revealing yourself as Mayor. Unlike the other abilities, this can be done with a real Mayor revealed/real Mayor can still reveal if you reveal.
If used during the Night, your options are:
Horseman - Announce a Horseman transforming the next day. Select which Acolyte, and when the next day starts, the transform message will appear. (obviously not a real horseman)
Attack - Announce a Basic Attack on a player. You may choose which cause of death you register as, but the attack is always a visiting Basic Attack. Your Death Note may or may not show depending on what cause of death you register as.