The archvile is perhaps the most versatile monster in the doom bestiary, which is part of the reason why he's my favorite baddie. While other monsters serve around 2-3 primary roles, he can serve around 4-6, making him perhaps the most threatening enemy there is. So using him well really depends on what kind of roles you want him to serve... and note that he can serve multiple roles as well. Others have already mentioned using him as a surprise baddie, a sniper and graveyard healer, but he can serve as a mix of these, as well as a panic-starter (warping him in then immediately having him warp away is the best way to freak out a player, putting them on edge), a fortifier (putting three AVs in one corner of the map on a ledge will keep the player away from there in a firefight), an ammo waster (letting him ressurect tougher monsters), and a monster who provides constant pressure (putting him in back of a bunch of demons will force the player to look for cover, letting the pinkies advance on his location so he can't merely outstrafe them).
Plus he's damn fast and durable, so nothing outside of a BFG will make the player feel safe in dealing with one. Because of that, he's a high priority monster (along with the Pain Elemental), forcing the player to act more recklessly when finding one, which you can always use to your advantage (for instance, an AV resurrecting revenants on the ground will distract the player from chaingunners on ledges). Remembering that the player will almost instinctively gun for the AV is one of the best aces up your sleeve you can have as a mapper.
More importantly than using them right however is not to use them wrong. Four AVs are usually overkill, while I find one or two the perfect amount (depending on what you're trying to do/how much cover there is, larger battles can handle three). Like the Pain Elemental they take a lot of ammo to eat through, and using one improperly to resurrect a host of barons is extremely annoying and can break the player's spirit. Also remember that since they need line of sight, so you should always provide a player with cover they can knowingly run to, as forcing the player to take a blast upon meeting one is a pretty egregious error (it's up there with chaingunners in a tower on the other side of the map and specters in pitch black rooms). It's a tough balancing act, but with more use (and useful feedback), you'll probably get a good feel for them soon enough.