Reference
The 6 conditions that go on a Pokemon rather than the field, with the exact figures the game uses. Several differ from what older generations taught you, so these are worth reading rather than assuming.
The Pokémon takes increasing poison damage at the end of every turn, starting at 1/16 of the Pokémon’s max HP, then 2/16, then 3/16, and so on. If the Pokémon switches out and reenters battle, the damage restarts at 1/16 of its max HP.
The Pokémon takes damage equal to 1/16 of its max HP at the end of every turn. The damage dealt by its physical moves is also halved.
The Pokémon can’t use almost any moves but has a 25% chance of being cured each time it tries to do so. The Pokémon will be cured on its third turn after becoming frozen or if it takes damage from a Fire-type move or certain other moves.
The Pokémon has a 12.5% chance of being unable to use moves. Its Speed stat is also halved.
The Pokémon takes damage equal to 1/8 of its max HP at the end of every turn.
The Pokémon can’t use moves other than Snore or Sleep Talk. After a Pokémon is put to sleep, it will remain asleep on its first turn, it will have a 1-in-3 chance of being cured on its second turn, and it will be cured on its third turn. A Pokémon that used the move Rest has no chance of being cured until its third turn.
Quoted from Pokemon Champions' own in-game descriptions.
Counter-play
The Pokémon is immune to status conditions and cannot become confused.
Halves the damage dealt by Dragon-type moves used against Pokémon on the ground. Pokémon on the ground are also immune to status conditions and cannot become confused.
Both are listed with every other field effect on battle conditions.
Questions
The Pokemon takes damage equal to 1/16 of its max HP at the end of every turn, and the damage dealt by its physical moves is reduced.
A 12.5% chance of being unable to use moves, and Speed is halved. The 12.5% figure is lower than several older generations used, so it is worth knowing exactly.
Poison is a flat 1/8 of max HP per turn. Badly poisoned escalates: 1/16, then 2/16, then 3/16 and so on. Switching out and back in resets it to 1/16.
Two field effects block them, though only one does so unconditionally. Safeguard: The Pokémon is immune to status conditions and cannot become confused. Misty Terrain: Halves the damage dealt by Dragon-type moves used against Pokémon on the ground. Pokémon on the ground are also immune to status conditions and cannot become confused.