How can you tell if a listed coin has been cleaned?

The short answer is that it is nearly impossible to determine whether a coin has been cleaned from a listing's photo. Only rarely do you find listings which show a coin in high enough magnification to determine whether it has been cleaned.

So, why are uncleaned coins more valued than coins which have been cleaned? 
Collectors value surfaces which are in as close as possible to the condition they were in when they left the mint. Being shiny or free of  A cleaned coin will never show the uncirculated, mint-state surfaces under a loupe or magnifying glass, as any traces of the original mint luster will be degraded or lost. And determining this requires only that you know a few things to look for under a magnifying glass or jeweler's loupe.

Cleaning is not so much an issue in heavily circulated (and worn) coins. But for better examples of coins, where you would expect some original surface to remain, cleaning becomes more of an issue. And it is important to value indeed in Proof and Uncirculated (Mint State) grades.

What evidences of cleaning can I look for?
First and foremost, you simply need to know what an uncleaned coin looks like. You won't be able to tell from a picture, but will once it is in your hands.

To get a feel for what an original, uncleaned surface should look like, take a magnifying glass and examine a few newly minted coins from the bank, noting the shimmer caused by minute radiating lines (this is called "cartwheel luster" - caused by the metal being squeezed when the coin is struck). This is very delicate, and is degraded or destroyed by most cleaning methods (which remove a bit of the metal).

A circulated coin that has no patination and seems too shiny will usually have been cleaned (and sometimes "whizzed" - an abrasive process which scratches fake cartwheel lines on the coin). There are books and websites which go into detail regarding signs of cleaning and whizzing. But nothing takes the place of examining genuine, uncirculated examples so that you have something with which to compare.

Circulated, cleaned coins will eventually re-acquire a patina that will somewhat mask the cleaning. But they will never be as highly valued as they would have been before the cleaning degraded the original surface.

And what can I do to avoid cleaned coins?
If the listing does not specify that the coin has not been cleaned, ask the seller if the coin has been cleaned. If the seller cannot tell you, then perhaps you should consider passing on the item being offered.

If the seller states in the listing that the coin has not been cleaned, or is in Uncirculated or Mint State, you should still ascertain that the seller allows you to return the coin if it turns out to have been cleaned. And buying from a seller who has good feedback, who has been selling for at least a year. Buy using PayPal, and pay PayPal using a credit card (which gives you 2 ways to dispute a fraud).

Some people prefer to buy slabbed coins which have been graded by a third party grader. Coins labeled as Proof, Mint State, or About Mint State should show no evidence of cleaning. However, slabbing is not an airtight guarantee that the coin is original. At best it is a second opinion that the coin is in the state printed on the label. At worst, these slabs can be counterfeits, with the slab itself masking evidence of cleaning. In between are huge numbers of slabs which have been certified by graders who are unqualified, who do not give more than a cursory glance at the coins which pass through their hands, and/or that habitually higher grades to coins than are warranted by their actual condition. A slabbed coin might be reassuring to some, but it is always the actual condition of the coin that counts - never the individual opinion printed on a label. You still need to know a bit about what you are buying.