>What does it require to describe a new species?  Who decides if it is
valid?  Is it possible for someone self-taught to get the job done?

Anyone can describe a new species as long as he/she does it properly.

To begin with, you need to take into account the criteria used to delimit
the already existing species in the genus your specimens belong to. For
example, snails species are usually based on shell morphology and/or
genitalia. So, if you are working with a genus in which the species
descriptions are based on genitalia, then it is best that you do the same
unless you can convincingly argue that your alternate criteria are better.

Then you need to make sure that your specimens do not belong to an already
described species, which means you need to know the existing species well.
Some species are notoriously variable. Variation may be induced by
ecological factors. In other words, individuals of a given species from
different locations may look different. So, having many specimens from
different places will help. Also, especially with land snails, watch out for
introduced species. Many times in the past, eminent malacologists described
"new species" based on specimens of introduced species which had already
been described from elsewhere.

The publication of a paper describing a new species only means that the
reviewers accepted it. It doesn't guarantee that the species will be forever
valid. Ten years from now someone may realize that what was described as new
in that paper was only an ecological variant, or an abnormal form, or a
hybrid, or whatever, of an older species. This happens all the time.

Hope this helps.

Aydin