A Monster Zoo is a large room completely filled with monsters.
There appears to be at least one Monster Zoo on each level after the first level. Be aware of this: if you've completed most of a level and haven't found the Zoo yet, every door you open could be it. On most systems, there will be a slight lag when you open a door to a Monster Zoo, as the game has to display 50+ sprites all at once. Be careful with this lag, as it's sometimes long enough for you to waste valuable turns accidentally clicking and thus moving in or out of the Zoo.
When encountering a Monster Zoo, there will be a Remaining Monster timer below the name of the area. An artifact is rewarded for defeating all the enemies.
Because of the massive amount of monsters, it is important to carefully weigh your tactical options as soon as you open the Zoo. Be careful to not accidentally click in the wrong place and charge into the Zoo, or you will quickly find yourself overwhelmed. Remember, the game is turn based, so as soon as you open the Zoo, plan as many moves ahead as you can.
One of your first goals should be finding an appropriate chokepoint, ideally near a Satanic Displacement Glyph or a set of upward stairs. Beware though, because going upstairs, downstairs or to your Pocket Dimension will cancel the remaining monster timer, as well as the artifact reward. If you can find one that leads the monsters through unsprung traps, even better. You can usually get about 10 to 20 monsters to follow you immediately, after which you need to head back closer to the zoo to get the rest of their attention.
If you have any Bolts of Mass Destruction (Bolts of Squid also work), firing one of them directly into the freshly revealed Zoo can quickly decimate the horde before many of them have a chance to chase you. It's important to save a few of these rare and expensive bolts for this purpose.
Once you find a chokepoint, load it up with the Area of Effect spells and items. Don't forget about your Puffballs, thrown bombs, bolts, and wands. Be careful not to overload a tile with too many effects or some of them may be removed. You want the horde of monsters to walk through as many tile based area effects as possible, such as poison, fire, and acid.
Do not waste any turns if possible. Eat buff food, eat recovery food, drink mana booze. Try to get as buffed as possible so when the mobs inevitably enter melee range, you can deal with them. If you've been carrying mushrooms, wands, or potions, and you don't know what they do, read up on them (in this wiki) before wasting turns trying them out.
Other than Lord Dredmor himself (and Vlad Digula in Diggle Hell - optional), Monster Zoos are as close to a "boss fight" as the game has, so be prepared to use all your items and skills to survive. Don't scout too far ahead after you've dealt with the initial stream of mobs - often you'll find yourself suddenly swamped right as your buffs run out.
If you're low on consumables, immediately retreat to a new level of the dungeon, preferably up. There you can restock on items and head back down later to deal with the horde. In a worst case scenario, you can hang out by the stairs and try to knock off one monster at a time, by attacking and retreating back up the stairs. This will help you clear out the zoo, but remember that leaving the area in any way (stairs, portals, Pocket Dimension, etc.) will prevent you from gaining the artefact, as it "ends" the event.