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Get to the Slayer Tower quickly using a slayer ring, else walk northwest from Canifis, or use the "C K S" fairy ring . Go up the spiked chain (level 61 Agility) and run southwest to climb the stairs. Go east and you're in the gargoyle room.
The Chaos Tunnels are arguably even more convenient, because the gargoyles are in the first room you enter when taking the rift entrance northwest of Edgeville. I still usually fight at the Slayer Tower though (force of habit?)
Kuradal's Dungeon is a good spot to fight these when on Slayer assignment; get there quickly using a ferocious ring; If you don't have a ring, use the fairy rings to code "B J Q", then run south and go up the stairs to Kuradal.
Equipment
You must bring a rock hammer (available from Slayer masters) to finish off each kill. A nose peg is also needed to get past the Aberrant Spectres, unless wearing a Slayer helmet (recommended when on assignment!)
Guthans armor is recommended for players without maxed stats; bring a faster weapon and switch to the warspear when needed. If using a healing familiar like a bunyip, though, you can get away with less armor.
Using Dharoks is faster, but watch your health -- these can do pretty good damage at times.
If you want to range or mage you will need to use a protection prayer; safe spotting is not effective because of the need to use the rock hammer to finish off the monsters.
Always wear a ferocious ring if fighting in Kuradal's Dungeon (which is only possible if these are your current Slayer assignment.)
Supplies
Bring a few cheap pieces of food if you have high levels and/or a healing familiar; bring better food otherwise. Super sets are recommended to speed up kills and drops, and reduce food consumption. Use Zammy brews instead of fighting with prayer.
A one-click teleport is always recommended if going to the Chaos Tunnels, in case of revenant attack. This is a multicombat area, so you can use combat familiars as well.
Bring about 10-15 nature runes per hour (they drop fires).
Familiar
If you are fighting with a normal weapon, a healing familiar means you need very little food here, and probably not Guthans either. If Dharoking, you can use a beast of burden for the unnoted bar drops, but frankly, you'll make more money by using a magpie for foragings and leaving the bars behind.
Combat Notes
With proper equipment, these aren't hard to fight, but many players have traditionally hated fighting them because of the need to click on the rock hammer and then click on the monster to finish it off. This is particularly annoying because of how the gargoyles bounce around as they fly. Fortunately, in 2009 Jagex added a right-click "Smash" option to gargoyles, so you no longer need to click on the rock hammer and then click on the monster. This is less hassle and also lets you fight a bit faster.
Note that you do not have to wait until the monster is completely red-barred before using the hammer on it; try when you see a couple of pixels of green remaining. If you do it too soon, you'll get a message and have to try again later, but you don't lose anything other than your time.
These monsters can be ranged or maged, but the need to run up and finish them off makes this rarely worth the bother. If you want to try, remember to use prayer or bring with food for when you get hit finishing them and grabbing drops.
Drop Notes
Gargoyles are not renowned as being particularly good drop monsters, but they actually provide three special items: granite mauls, dark mystic robe tops, and adamant boots. The maul is quite valuable these days, so getting even one can make for a nicely profitable trip.
In addition to the special items, gargoyles drop steel and mithril bars (sadly, unnoted), gems, rune full helms, lots of fire runes, and noted pure essence. They are also good blue charm droppers.