Thanks, both of you! I now have a notepad doc titled "How to Play an Archer" on my desktop.
(Seriously, I really do.)
Well, then. 
Your priority will be to max out the Archery tree, upgrades included. Skill upgrades are very important, they turn simple arrow shots into stun-locks, AOE, etc. But aside from that, you can also dump a few points into the Sabotage tree and the Subterfuge tree. From Sabotage, Poisoned Weapons is very interesting for an archer, because it gives you damage over time that you don't otherwise have (since Bleed effects are broken and don't actually work in the game). You can also get Infected Wounds, Fighting Dirty and Explosive Toxin when you start having leftover points you don't know what to spend on. Caltrops is a waste, doesn't really seem to do anything useful. Under Subterfuge you may want Evasion and Evade if you keep getting cornered and mobbed. You'll get the hang of how to not get cornered eventually, but meanwhile Evade can be useful to avoid a punch in the face on the last minute.
My favorite way to start any combat is by locating the mages or archers among a group of enemies and sniping them from a distance with Full Draw. Poisoned Weapons + Full Draw = mages and archers dead on the floor before the rest of the enemies even see you, now you only have meleers left to handle (and if you're smart and never ever leave the house without Blackwall or Cassandra with War Cry, your tank(s) will be right on top of that).
Depending on the difficulty you're playing, you will have to craft your own bows, no way around it. The bows you'll find out in the world, both in loot and in vendors, are bollocks, you can craft better Tier 1 bows at level 4 than you'll find in loot at level 20. Crafting your own bows is awesome, though, as you can use all sort of nasty tricks on them, like chance to use Hidden Blades, or +3 Guard On Hit etc, so you'll have fun with that.
And strafe!!!!! Strafe, strafe, strafe. The most important thing you'll ever do as an archer is strafing. Stafe!