For a history of decimal fractions see Smith's History Of Mathematics, vol II, pp. 238ff. In the Middle East, Smith gives credit to al-Kashi (c.1400), but the relevant algorithms, in a table notation, appear already in al-Samawal (c.1150), see Katz's History of Mathematics, 7.2.3.
Notationally, the fractional separator was initially a bar placed over the digit of units, which was later replaced by a point, possibly for ease of printing. Pellos used the decimal point in print already in 1492, but Cardano still used a bar in 1539. However, neither Pellos nor Cardano appreciated the algorithmic significance of the separator in calculations. According to Smith, the first man to do so in Europe was Rudolff, who performed a sample calculation in Exempel Büchlin (1530). He also used the bar rather than the decimal point, and his work was not appreciated at the time. Smith does not mention della Porta, but his use was likely purely notational, a la Pellos.
The first comprehensive explanation of decimal fraction calculations in Europe is indeed due to Stevin's De Thiende (1585), and after him they became more common. But their final triumph only came after the invention of logarithms by Napier. However, Stevin did not use either the bar or the point, and his notation was, in fact, quite unwieldy: he wrote the power of $1/10$ in a circle after each digit (see facsimile in Smith, p.243). The propagation of the modern notation was due to Bürgi, Kepler, Beyer and Napier. Bürgi used a dot or a comma, and his example was followed. Napier did not use the decimal point in his original publication of the logarithmic tables in 1614, but it appears in their English translation by Wright (1616), and Napier adopted it in Rabdologie (1617). Kepler and Beyer used both comma and $','',''',''''$ placed over digits (as in the ancient sexagesimal notation) in 1616. Here is from Smith:
"Another influence leading to the invention of the decimal
fraction was the rule for dividing numbers of the form $a\cdot10^n$,
attributed by Cardan (1539) to Regiomontanus... Borghi (1484) elaborates
this rule, but it appears in its most interesting form in the rare
arithmetic of Pellos (1492), who unwittingly made use of the
decimal point for the first time in a printed work (p. 239).
The use of the dot before and after integers had been common
in the medieval manuscripts, as in the case of Chuquet's work
already mentioned, but its use to separate the integer from
what is practically a decimal fraction is first seen here. Later
writers commonly used a bar for this purpose, as was the case
with Rudolff (1530; see page 241), Cardan (1539), Cataneo
(1546), and various other writers... Pellos, however, did not recognize the significance of the decimal point, as is evident from the facsimile on page 239, and no more did Cardan appreciate the significance of the bar that he
used for the same purpose.
[...] The first man who gave evidence of having
fully comprehended the significance of all this preliminary
work seems to have been Christoff Rudolff, whose Exempel-
Büchlin appeared at Augsburg in 1530. In this work he solved
an example in compound interest, and used the bar precisely
as we should use a decimal point today (see page 241). If any
particular individual were to be named as having the best rea-
son to be called the inventor of decimal fractions, Rudolff
would seem to be the man, because he apparently knew how to
operate with these forms as well as merely to write them, as
various predecessors had done. His work, however, was not
appreciated, and apparently was not understood, and it was not
until 1585 that a book upon the subject appeared.
The first to show by a special treatise that he understood the
significance of the decimal fraction was Stevin, who published
a work upon the subject in Flemish, followed in the same year (1585) by a French translation. This work, entitled in French
La Disme, set forth the method by which all business calculations involving fractions can be performed as readily as if they
involved only integers. Stevin even went so far as to say that
the government should adopt and enforce the use of the decimal system, thus anticipating the modern metric system. He was the first to lay down definite rules for operating with decimal fractions, and his treatment of the subject left little further to be done except to improve the symbolism... The improvement in the symbolism was
due largely to Bürgi, Kepler, and Beyer, and to the English
followers of Napier... It is unquestionably true that the invention of logarithms had more to do with the use of decimal fractions than any
other single influence."
