How do I use the “Barbara, Celarent, … etc.” mnemonic?

[Geremia]

From here:

Medieval logicians memorized this most famous logic mnemonic:
Barbara, Celarent, Darii, Ferio ← direct first figure
 Baralipton, Celantes, Dabitis, Fapesmo, Frisesomorum ← indirect first figure
 Cesare, Camestres, Festino, Baroco ← second figure
 Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison ← third figure
The 3 vowels of each name represent the 4 possibilities of the square of opposition:

So Barbara is an AAA syllogism, e.g.:

• Every man is an animal.
• Every animal is a creature.
• ∴ Every man is a creature.

There is more to the mnemonic than this. Apparently the consonants in the names allow one to reduce the corresponding syllogism to that of a simpler figure.
Are there any references that overview how to fully use all that is packed into this very elaborate, well-thought-out mnemonic?

Answer:

Explanation of the Mnemonic
Brody, Boruch A. "Logical Terms, Glossary of." Encyclopedia of Philosophy. Ed. Donald M. Borchert. 2nd ed. Vol. 5. Detroit: Macmillan Reference USA, 2006. 533-560. Gale Virtual Reference Library. Web. 19 May 2016.:

mnemonic terms
The names that the medieval logicians introduced for the valid syllogisms. One such term is "Barbara." The key for these mnemonics is as follows: The three vowels respectively indicate the three constituent propositions of the syllogism as A, E, I, or O. For first-figure syllogisms the initial consonants are arbitrarily the first four consonants; for the other figures the initial consonants indicate to which of the first-figure syllogisms the syllogism in question may be reduced. Other consonants occurring in second-, third-, and fourth-figure mnemonics indicate the operation that must be performed on the proposition indicated by the preceding vowel in order to reduce the syllogism to a first-figure syllogism. The key for this is as follows: "s" indicates simple conversion, "p" indicates conversion per accidens, "m" indicates metathesis (interchanging of the premises), "k" indicates obversion, and "c" indicates convertio syllogism (that is, the syllogism is to be reduced indirectly). In mnemonic terms the only meaningless letters are "r," "t," "l," "n," and noninitial "b" and "d." More elaborate mnemonics have been devised for syllogisms in which two or more of the premises exhibit modality. See entry "Logic, Traditional."
Mnemonic Terms

Name        Figure      Major   Minor   Conclusion
                        premise premise
Barbara     first       A       A       A
Baroco      second      A       O       O
Bocardo     third       O       A       O
Bramantip   fourth      A       A       I
Camenes     fourth      A       E       E
Camestres   second      A       E       E
Celarent    first       E       A       E
Cesare      second      E       A       E
Darapti     third       A       A       I
Darii       first       A       I       I
Datisi      third       A       I       I
Dimaris     fourth      I       A       I
Disamis     third       I       A       I
Felapton    third       E       A       O
Ferio       first       E       I       O
Ferison     third       E       I       O
Fesapo      fourth      E       A       O
Festino     second      E       I       O
Fresison    fourth      E       I       O

Reduction
So, what are the different types of reduction mentioned above?

• simple conversion
• conversion per accidens
• metathesis (interchanging the premises)
• obversion
• convertio syllogism (indirect conversion)

reduction of syllogisms
The process whereby syllogisms in imperfect figures are expressed in the first figure. Reduction is direct when the original conclusion follows from premises in the first figure derived by conversion, obversion, etc., from premises in an imperfect figure. Reduction is indirect when a new syllogism is formed which establishes the validity of the original conclusion by showing the illegitimacy of its contradictory. See entry "Logic, Traditional."

conversion
In traditional logic, a type of immediate inference in which from a given proposition another proposition is inferred that has as its subject the predicate of the original proposition and as its predicate the subject of the original proposition (the quality of the proposition being retained). The process of conversion yields an equivalent proposition only when the original proposition is an E- or I-proposition; when it is an A-proposition traditional logicians allowed for conversion per accidens (or by limitation)—that is, conversion plus a change in the quantity of the proposition from universal to particular. Thus, the E-proposition "No men are immortal" yields "No immortals are men," but the A-proposition "All men are mortal" can be converted only by limitation, yielding "Some mortals are men." The process of conversion yields no equivalent proposition if the original proposition is an O-proposition. See entry "Logic, Traditional."

obversion
In traditional logic, a type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, and whose quality is affirmative if the original proposition's quality was negative and vice versa. Obversion of a proposition yields an equivalent proposition when applied to all four types (A, E, I, and O) of propositions that traditional logicians considered. See entry "Logic, Traditional."

Also, see the International Society of Scholastics's The Science of Logic: A Course in the Formal and Material Principles of Right Reason in the St. Isidore e-book library