Hi Mathman and welcome to the forum! Plenty of friendly people here and all willing to share their collective expertise.
There's two basic types of fake Morgans: (1) those which copy less common and hence more valuable Morgans such as many from the Carson City (CC) Mint, e.g. 1889CC, 1893CC, 1879CC. These are intended to deceive collectors of rare coins; most are purportedly in mint condition or higher circulated condition. And (2) those which are/were intended for circulation and/or the La Vegas slot machines. The latter are currently much less common and than the former since Morgans are no longer used either in circulation nor in slot machines; these are seldom offered on
ebay.
Most fakes are cast copies and, in hand probably wouldn't fool many people since they look "funny" and generally weigh noticeably less than an authentic Morgan. The surfaces are dull with a "leaden" appearance (due to the lead used to keep the weight up) and the fields (flat parts of the coins) have a graininess due to the casting. There is no "cartwheeling" (reflects light) to most fake Morgans. The problem is with buying coins from pictures which makes detection more difficult but, with exceptions not impossible.
More recent counterfeits of less common Morgans may be of more sophisticated construction using stamping techniques and actual silver. A few will fool even experts, but these are very uncommon. If one does not know Morgans all that well but is interested in investment or high grade coins, buy only authenticated and encapsulated (slabbed) coins by the top third party grading services, i.e., ANACS, NGC, PCGS, and ICG.
Many, many contemporary counterfeits originate from China and one should view all Morgan auctions originating in China with a cynical eye. We Morgan nuts usually (but not always) spot the obvious and less obvious fakes on
ebay and promptly report them. Unless they're a one- or three-day auction,
ebay normally responds and pulls the auctions. This subject on safe coin shopping on
ebay needs amplification, but there's neither time nor space here. See the Auctions forum section. For common date and mint mark Morgans on
ebay, almost all raw (unslabbed) Morgans are authentic (problems such as cleaning and damage notwithstanding) since the real money in counterfeits is to be made with the uncommon and rare dates and mintmarks. Buy only from established dealers and sellers with good feedback.
Bottom line: educate yourself on Morgans before buying. A good start: Q. David Bowers'
Official Red Book of Morgan Silver Dollars.