Any given corpse can only be exploited once (although a creature that is resurrected and dies again leaves an unexploited corpse, except with Unyielding Aura (PvP)). This means that you may be competing both with enemy and allied necromancers to make use of corpse-based magic. If teaming with other necromancers, do your team a favor and communicate about the spells you will each be using. Likewise, when fighting in areas where enemy necromancers abound, it is often useful to carry a fast casting corpse spell to prevent your enemies from using them against you (Corpse denial). You may also wish to take advantage of equipment that allows you to cast these spells faster. These include Bloodstained Insigina and weapons or focus items that grant bonuses to casting speed for the respective attributes.
You can begin casting corpse exploitation spells with multi-second casting times about 1 second before there is a corpse available. Paying close attention to the health bar of your opponent and casting just before his death will help you get to that corpse before the enemy does.
Necrotic Traversal is a very effective way to shutdown all available corpses of being exploited, as it is the corpse-targetting skill with the fastest activation time (3/4 second). A wise use of this skill can really hurt an enemy Necromancer relying heavily on corpses.
It is not necessary to directly target a corpse to make use of it. In general, if you do not have a target, the corpse closest to you will be used. If you have an enemy or ally targetted, then the corpse closest to your target would be used.
You must be within standard casting range of a corpse when you cast the spell. You will not automatically run to the nearest corpse to get close enough. Attempting to cast corpse-based spells when too far away from a corpse will result in an "invalid target" message. No energy will be lost, however.