This improv system works for systems with ascending AC--where the foe's AC is your target number on a d20...Like Penny, Nickel, Dime, Quarter, Dollar it isn't perfect, but it has stood me in good stead through many random encounters and is a useful thing to have around as a last resort if you do a lot of improvisation when DMing.
So you got all of a sudden a monster but--d'oh--no stats because it was just unexpectedly summoned or invented.
So this: roll d20 to hit, but when you roll that, also roll another die: if it's like a relatively wimpy monster like a goblin chief roll a d4, if it's like Beelzebub or what-all, roll a(nother) d20, and if it's something in between, roll a die whose value's in-between. Like if it's a troll roll d12.
Add the 2 dice together--that's the monster's total to-hit roll this round. Nothing to write down--if it's, for example, a d8 monster (say, a gargoyle) you just roll a d8 with that d20 every time. Its "bonus" will vary every round.
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Basically, if you're scaling the adventure to the PCs, choose the die where the high end matches or slightly exceeds the toughest player's bonus, and if it's a boss go two or more dice up. If you're not scaling just use the die equal to twice where you'd put the monster on a toughness scale from 1-10.
The scale's easy to remember because you stare at it the whole time you're DMing: d4, d6, d8, d10, d12, d20.
And if you wanna be super lazy, you can use that second die as its damage roll, too.
This all ignores a lot of detail that separates one monster from another, but if you need a "hideous mutant from the bottom of the spawning chamber" out of nowhere all of a sudden, you can do worse than (say) 8 hd/d20+d8 to hit/d8 damage and sort the rest out if and when it comes up.
If it was fighting 3.5-style PCs I'd give it 2 attacks or a +8 bonus to damage, too.
