Teaching grandmother to suck eggs is an English-language saying, meaning that a person is giving advice to someone else about a subject that they already know about (and probably more than the first person).

Origins of the phrase

The origins of the phrase are not clear. The OED and others suggests that it comes from a translation in 1707, by J. Stevens, of Quevedo (Spanish author):

"You would have me teach my Grandame to suck Eggs"

Recorded usage

• Its use was recorded in Tom Jones
  The History of Tom Jones, a Foundling
  The History of Tom Jones, a Foundling, often known simply as Tom Jones, is a comic novel by the English playwright and novelist Henry Fielding. First published on 28 February 1749, Tom Jones is among the earliest English prose works describable as a novel...
  
  by Henry Fielding
  Henry Fielding
  Henry Fielding was an English novelist and dramatist known for his rich earthy humour and satirical prowess, and as the author of the novel Tom Jones....
  
  , published in 1749:

“I remember my old schoolmaster, who was a prodigious great scholar, used often to say, Polly matete cry town is my daskalon. The English of which, he told us, was, That a child may sometimes teach his grandmother to suck eggs”

• Letter from Percy Bysshe Shelley to Leigh Hunt, 8/15/1819:

“But what am I about? If my grandmother sucks eggs, was it I who taught her?”

• The phrase was used in the 1890s in a Punch
  Punch (magazine)
  Punch, or the London Charivari was a British weekly magazine of humour and satire established in 1841 by Henry Mayhew and engraver Ebenezer Landells. Historically, it was most influential in the 1840s and 50s, when it helped to coin the term "cartoon" in its modern sense as a humorous illustration...
  
  magazine cartoon:

"You see, Grandmama, before you extract the contents of this bird's egg by suction, you must make an incision at one extremity, and a corresponding orifice at the other." Grandmama's response is to the effect, "Dearie me! And we used to just make a hole at each end."

• In "Hog on Ice" (Harper & Row, New York, 1948), Charles Earle Funk says:

"To teach one's grandmother to suck eggs - To offer needless assistance; to waste one's efforts upon futile matters; especially, to offer advice to an expert. This particular expression is well over two hundred years old; it is just a variation of an older theme that was absurd enough to appeal to the popular fancy.

• The phrase has been used in the movie The Big Country
  The Big Country
  Meanwhile, Terrill insists on riding into the canyon. Initially, Leech refuses to accompany him, and the other men follow his lead. However, after Terrill rides out alone, Leech catches up with him. The remaining hands again align themselves with Leech by following. The group soon rides into a trap...
  
  :

"Go teach your grandmother to suck eggs! I've been handling guns like this, flintlock and caplock, since before you were born."

• The line was also used in the sixth episode of the first season of The Ren & Stimpy Show:

"I don't think you're happy enough! That's right! I'll teach you to be happy! I'll teach your grandmother to suck eggs! Now, boys and girls, let's try it again!"

• Egg sucking is the subject of this parody of a military instruction: How to Suck an Egg

"The purpose of this exercise is to follow precise unnecessary directions issued by a higher HQ. You have been directed to be in possession of a fresh empty eggshell for no apparent reason. Simple issuance of tasks being insufficient in any anal-retentive, career-oriented, hopelessly bureaucratic military staff society, the staff of the higher HQ have issued the following instructions."

• Sméagol instructed his grandmother, as related in the Riddle Contest in Chapter Five of The Hobbit
  The Hobbit
  The Hobbit, or There and Back Again, better known by its abbreviated title The Hobbit, is a fantasy novel and children's book by J. R. R. Tolkien. It was published on 21 September 1937 to wide critical acclaim, being nominated for the Carnegie Medal and awarded a prize from the New York Herald...
  
  :

"But suddenly Gollum remembered thieving from nests long ago, and sitting under the river bank teaching his grandmother, teaching his grandmother to suck — ‘Eggses!’ he hissed.

Related phrase

The use of the phrase "Suck-egg" for "a silly person" dates back to 1609, in the OED.