Tactics vs Flying creatures
Basic Rules
If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of its ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as the fly spell. - PHB pg191, under "Flying Movement"
Falling creatures fall 500 feet on the first round, and a 1,000 feet every round thereafter.
Falling damage is 1d6 per 10 feet speed, and capped at 20d6 (thus any height 200 ft+ is 20d6, average 70 dmg).
Grappling
A grapple ends if the target is moved out of the grappler's reach.
Grapple Houserule: For purposes of grappling, monsters with Str 15+ are treated as proficient in Athletics (Dex 15+ are treated as proficient in Acrobatics). This means you can use their attack bonus as a grapple check.
Harpy +1
Gargoyle +4
Griffon +6
Young Dragon +7 (large)
Adult Dragon +11 (huge)
Physical Size: Grid sizes don't represent the physical size of a creature, just the space it controls on the battlefield. - PHB pg191 "A creature's space is the area in feet that it effectively controls in combat, not an expression of its physical dimensions. A typical Medium creature isn't 5 feet wide, for example, but it does control a space that wide. If a Medium hobgoblin stands in a 5-foot-wide doorway, other creatures can’t get through unless the hobgoblin lets them."
Dragons
Spellcasting Variant: spells equal to Charisma modifier (max spell lvl = 1/3 CR round down) - MM 86
CR 3 (1st lvl): feather fall (reaction, drops 60 ft/round)
CR 6 (2nd lvl): misty step (bonus, get out of forcecage)
CR 9 (3rd lvl): counterspell (reaction, blocks spell, 60 ft vs visible caster)
CR 12 (4th lvl): freedom of movement (1 hour, blocks magical impediments)
CR 18 (6th lvl): true seeing (1 hour, spots ethereal)
CR 24 (8th lvl): Anti-magic (blocks all spells)
Adult Dragons get Legendary Resistance 3/day (auto save).
Dragon size - Draconomicon 3.5 pg56 (Large dragon weighs 2,500 lbs and is 31 feet long)
Non-magical Tactics vs Flyers
Grapple: Can fall with falling flyer. Otherwise, flyer can start flying as soon as grapple ends.
Athletics (5th lvl, Str 18, +7) + Jump + Grapple: Allows jumping up to grapple a creature 16 ft in the air [(3+Str mod)+(6 ftx1.5)]. Success on Str+7 lets you bring the flying creature down to the ground without taking damage yourself (unless your speed is reduced to 0). A flying creature may hesitate to come lower than 20 ft off the ground, when seeing a muscular medium creature since the medium creature could jump around 15 ft high without magic.
Shoving: Normally shoving can knock you prone (when standing on the ground). Since there is no ground under a flying creature, a shove would push it 5 ft lower if aimed down.
Net (15 ft, attack with disadvantage, restrained): Only usable on large or smaller. If you can get within range and successfully hit, it's a great way to make a flying creature fall.
Battle master + Longbow (150 ft) + Trip Maneuver (Large or smaller, Str sv, prone): Only usable on large or smaller. This maneuver requires a successful attack roll plus a failed Str sv for the flying creature to fall. Great method, since with two hand crossbows, a 3rd lvl battle master can make upto 3 attempts to trip a flyer. By 7th level, you could get 5 possible attempts in a round.
Spell Tactics vs Flyers
No reactions allowed (such as Counterspell/Feather Fall), if cast during a surprise round.
Short range (30 ft or less):
No reactions allowed (such as Feather Fall).
Tasha's Hideous Laughter (1st lvl, 30 ft, Wisdom sv, prone & incapacitated): Great way to make a flyer fall. Doesn't effect creatures with less than Int 4 (such as Griffons).
Medium range (35 ft - 90 ft): may be beyond counterspell range (60 ft)
Enlarge (2nd lvl, can grapple huge, adv Athletics) + Jump (1st lvl, allows x3 height) + Athletics (5th lvl, Str 18, +7) + Grapple: Allows jumping up to grapple a creature 39 ft in the air [3x(3+Str mod)+2x(6 ftx1.5)]. Success on Str+7 (advantage) lets you make the flying creature fall to the ground without taking damage yourself (unless your speed is reduced to 0). This tactic very likely requires the combined tactics of a spellcaster (with the right spells) and a trained grappler, along with some preparation (enlarge). A flying creature may hesitate to come lower than 30 ft off the ground, when seeing a large creature since a large creature could jump around 25 ft high without magic [(3+Str mod)+2x(6 ftx1.5)].
Fly (3rd lvl, speed 60 ft): With this spell, would not need the jump spell and could follow the grappled falling target to the ground without taking damage (as long as he doesn't run out of speed). Since this is a concentration spell, you would need two spellcasters and a grappler to pull this off.
Web (2nd lvl, 60 ft, Dex sv, restrained and falls for 1 round): Great way to make a flyer fall.
No reactions allowed (such as Feather Fall).
Hold Monster (5th lvl, 90 ft, Wis sv, paralyzed): Great way to make a flyer fall.
Power word stun (8th lvl, 60 ft, 150 hp, no save, stunned): Great way to make a flyer fall, after softening up target. Finishing move if flying.
No falling damage
Command [Land] (1st lvl, 60 ft, Wisdom sv, On its turn target lands and then ends its turn): Good way to bring down a intelligent flyer that understands your language. However, doesn't cause any falling damage and doesn't keep them on the ground after this round.
Long range (95 ft +): generally can be cast beyond counterspell range (60 ft)
Ensnaring Strike (1st lvl, oath of ancients paladin or ranger, must hit, Str sv [adv if Large], restrained) + Longbow (150 ft): This spell requires not only a successful hit, but then assumes a flying creature (mostly large+) will fail a Str sv (with advantage) and fall. A miss, does allow you to keep the spell going for later.
Conjure Elemental [Air] (5th lvl, CT 1 minute, Str sv, prone): Cast ahead of time. With low strength, unlikely to trip a strong flying creature. Whirlwind vs Str sv may work to make a flyer fall.
Bigby's Hand (5th lvl, 120 ft, contested Str +8, carrying capacity 1,560 lbs, speed 60 ft, grappled): The hand can hold a medium (or smaller) dragon in mid-air, but it can't keep up with a falling dragon. The hand loses its grip as soon as the dragon falls beyond 60 ft (it's speed), at which point the dragon's speed ceases to be 0 and it can fly again.
Etherealness (7th lvl, 8 hours, can move vertically, possible surprise round) + Otto's Dance (6th lvl, 30 ft, no save, cant move): Great tactic make a flyer fall.
No falling damage
Earthbind (2nd lvl, 300 ft, Str sv, descends 60 ft/round): Great long range way to bring down a flyer. However, doesn't cause any falling damage.
Forcecage (7th lvl, 100 ft, 20 ft cage, no save, trapped): Physical size must fit into forcecage dimensions, not just the area it controls on battlefield (a large dragon is too long).
Flyer Tactics
Fly down + Grapple + Fly up (half-speed while grappling unless huge) + Drop: That means a wyrmling black dragon (speed 60) could fly down 20 ft, make a grapple check +4 to grab a PC, lift him up 20 ft, and drop him for 2d6 damage. If the wyrmling chose on the next round, it could use the dash action to lift the PC another 60 feet (total 80 ft), and then drop him for 8d6 damage (alternatively, it could lift him another 30 ft (total 50 ft), breathe acid on him (5d8, save for half), and then drop him for 5d6.
Fly down + Breath Weapon + Fly up: A wyrmling black dragon starting at 45 feet off the ground, could fly down 30 ft, breathe acid, then fly up 30 ft (ending up 45 feet off the ground again). This could easily end up with it behind cover and requiring the PCs to use readed actions (reactions) that would limit their number of return attacks to 1.