comparing the internal coloration can help if broken
you must know what the wall structure coloration is in an original, with variations, from that area/time
edit: also the density of the wall is different depending on the manner of construction (coiled, etc.)
Go to school, study, study, study, examine thousands of examples in museums and become an expert. Sorry, there is no other way. Most, perhaps well over 90% of meso and south American pottery pieces that come on the market are fake, they are things to stay away from unless you are an expert. The indigenous people of central and south America have been faking pottery items at least since the 1950s so most of what we see for sale in this country are fakes. Japanese sword collectors have a saying that out of every ten Japanese swords for sale eleven are fakes, it is a similar situation with pottery artifacts from below our border. A lot of pottery artifacts from the mideast and asia are now being faked too, dog eat dog world out there and faking pottery is a simple task. On my first trip to Mexico around 1962 I saw lots of people standing along roadsides selling terracotta objects that were "muy antigua" and all fake. I was lucky enough to get to dig around a bit back then and did find lots of original sherds, obsidian blanks for making blades, and some other cool things. One cannot go there and do this anymore.
No, still no quick and easy way. When it comes to Etruscan repros and fakes, they have been doing that a lot longer in Italy longer than Mexico I think. I have a repro Etruscan pottery sculpture that my parents bought as a repro in the late 1940s. It is always possible that you have a real and valuable item but if it is real and valuable you should have no problem paying for a proper professional appraisal.
The style. I actually made a thread with photos under the “What is it?” section but didn’t get many responses. It’s not exactly the prettiest piece but I’d be interested in hearing your guys’ thoughts:
interesting, but am not even qualified to spout an opinion
edit: don't think is Etruscan;
the hairstyle is distinct, as is the patterned headband and triangular face - something to look for
the eyes are not correct and it was not painted
I sent the pictures to Bob Dodge who is a well-known antiquities expert and appraiser (I saw him on Pawn Stars and tracked down his contact). He says it appears real and Etruscan to him based on the photos but says a TL test is needed to say for certain. That test runs about $400. A bit of a gamble as I’ll be flushing that money away if it turns out not to be real and have no idea what the value would be if it is. Glad to hear it has potential though!