The record trade has used broadly the same ladder for decades, and it is unusually precise once you learn it.
The ladder
Mint (M) — perfect, effectively unplayed. Used sparingly by honest sellers. Near Mint (NM) — looks and plays as new. Very Good Plus (VG+) — light handling marks, plays without distracting noise. Very Good (VG) — visible marks and audible surface noise, but it plays through. Good (G) — plays, with significant noise. Good means worn. Poor (P) / Fair — damaged, for completeness or parts.
Two objects, graded separately
Written disc/sleeve: VG+/VG is a very good plus record in a very good sleeve. A single grade is ambiguous and should be questioned.
For the disc: hairlines, scuffs, scratches you can feel, groove wear, warp — and whether a mark is audible, which is what the grade is really about.
For the sleeve: ring wear, seam splits, corner wear, writing, stickers, water marks.
There is no third-party service for most records
Grading here is done by the seller, against a published ladder, which is why the ladder matters so much. A seller who says "9/10" is not grading; they are guessing in a different language.
What to state outside the grade
Whether you played it and what it sounded like. Whether it has been cleaned. What is missing — inner sleeve, insert, poster.
Sealed records
Graded as sealed and nothing more. You cannot grade a surface you have not seen, and saying so is the honest answer. Describing records.
Questions people ask
Can a record be mint if played once?
Most sellers would call that near mint. Mint implies unplayed.
Does surface noise mean a bad record?
It means a lower grade. Plenty of people buy VG records at VG prices happily.
Is the sleeve grade less important?
Usually, and it is still half the description.
More: buying records, what they are worth.