You are not going to find a painting by Giorgione, named as such, on eBay: I've just had a look and see no one has had the gall to offer one at the time of writing. But genuine works of art by less rare names are advertised on eBay and are there to be bought. Care needs to be taken and there are some symptoms to look out for which flag up auctions to avoid.
I am going to discuss Modern British Art because it is a popular collecting area with a plentiful supply and keyword searches should return examples of moderately well-known artists' work.
If you want to see what is available in this area here are some random names to search for: Henry Moore, Jacob Kramer, Augustus John, Duncan Grant, Mark Gertler, Stanley Spencer, Dora Carrington, Vanessa Bell. Do a phrase search in titles and descriptions with an artist's name in quotes: eg "Mark Gertler". In this case all the results should be Mark Gertler items. If another artist's work appears in the list then a seller is probably KEYWORD SPAMMING, luring bidders into a dangerous auction they should not have found with the search used. Serious collectors looking for bona fide auctions of a particular artist's work should use title-only keyword searches using the artist's name; a bona fide auction of a Henry Moore will be named as such in the title.
Looking for underpriced works by known artists among anonymous or incorrectly identified works involves protracted category browsing and sophisticated keyword searches without personal names. Remember that if no claim is made about the creator of a painting in the title or description the seller can't be blamed if you make a mistake about the artist's identity.
Illiteracy in an auction description, by itself, is not a reason for avoiding an item. If an important keyword is misspelled you might be the only bidder who finds an item. However, art dealers and collectors are usually highly educated and you don't expect to see, e.g., " a auction" or "a artist" (examples found on eBay in several auctions from the same seller). You would wonder whether the seller is a reliable informant who has read a single art book in his life. So bad spelling and grammar should you put you on your guard. Art fraud is however more likely to be a "white collar" crime.
I don't go along with the theory that "if the low price is too good to be true then it probably isn't". There is a culture on eBay of competitive pricing and I sometimes find that in order to get the bidding going I need to start low. However, for a seller to have a brimming stream of good art at low prices is suspicious and you should question where the pictures are coming from and what they are.
Often the authorship of a painting is uncertain and a conjecture is reasonable and all anyone can give you. But an art dealer is exceptionally unlucky if none of his eBay listings can be unequivocally stated to be by the artist mentioned the title or description. Look out for such prevaricating phrases as "signed by, or inscribed, Henry Moore" and divide the price by 100,000 if it is only "inscribed". Most Modern British Artists' work is still under copyright and so names cannot be applied to works without permission or good reason and incorrect attributions will offend against eBay's VERO (verified rights owners) rules.
Sometimes a listing for art on eBay contains an extensive screed arguing for an attribution the auctioneers and museums have been too stupid or corrupt to think of, or back. Avoid.
Art market coups are made on eBay but usually by market insiders and experts. One instance I know of was a Norwich School etching, by Chrome the Elder, correctly identified as such by the eBay seller and which made a respectable £1000 on eBay: it was sold on instantly for £6000 by the buyer who knew it was exceedingly rare.
Contemporary subversive and jokey British art by the likes of Banksy, Damien Hirst and Jamie Reid is sought for and is apparently listed on eBay but due to the nature of the material it is hard to ascertain the authenticity and collectors are better to buy from properly catalogued auctions or the artists' representatives.

Especially in combination, these things should put you on your guard:
"inscribed or signed" : the seller knows it is not a genuine signature.
Spam: in a spammed proper name search return you've been tricked into looking at A when you went looking for B.
Too copious supply: is he pilfering a collection?
Red herrings: a long description. It is larded with hints to allow you to draw your own wrong conclusions and you don't notice he has misssed out something vital.
Where is it from?: the seller doesn't just buy stuff down the market.
Disclaimers: all the seller's items have "get out" clauses and in no case is he unequivocal about the authorship.