As explained in Hatarat Nedarim a person should do this as an individual in front of a bais din of three people.
Hatarat Nedarim – Annulling Vows Before Rosh Hashanah and Yom Kippur
It is customary to conduct “Hatarat Nedarim” – the formal annulment of
vows – before Rosh Hashanah and before Yom Kippur. This declaration is
made in the presence of three people that serve as a Bet Din
(Rabbinical court). It absolves a person from vows he made and from
customs which he accepted upon himself. Preferably, a person should
perform Hatarat Nedarim in the presence of ten men, as this kind of
Bet Din has more authority than a three-member Bet Din.
As part of the Hatarat Nedarim declaration, a person says that
although Halacha requires a person to specify the particular vows
which he wishes to annul, he is unable to do so because they are too
numerous. The work Derech Ha’haim cites from the Shiboleh Ha’leket
(Rav Sidkiya Ben Abraham, Italy, 1230-1300) that this special
provision applies only to vows of which a person is unaware. One can
earn annulment for these vows by informing the Bet Din that he cannot
recall his vows. If, however, a person is aware of a certain vow or
custom from which he wishes to absolve himself, then he must specify
it when he makes the Hatarat Nedarim declaration.
This is better as it shows that a person has been careful about oaths and would not rely on the general statement.
The readiness with which vows were made and the facility with which
they were annulled by the scribes gave the Karaites an opportunity to
attack the Rabbinites, and forced the Geonim to minimize the power of
dispensation. Yehudai Gaon of Sura (760), author of the "Halakot
Pesuḳot," went so far as to forbid any study whatsoever of Nedarim,
the Talmudic treatise on oaths (Alfasi on Nedarim, end; L. Löw, l.c.
p. 363). Thus the "Kol Nidre" was discredited in both of the
Babylonian academies and was not accepted by them (S. K. Stern, in
"Ḳebuẓat Ḥakamim," ed. Warnheim, 1861), as is affirmed by the geonim
Naṭronai (853-856) and Hai Bar Naḥshon (889-896; Müller, "Mafteaḥ," p.
103; Cassel, "Teshubot Geonim Ḳadmonim," p. 9; Zunz, "Ritus," p. 189;
Ṭur Oraḥ Ḥayyim, § 619; "Kol Bo," § 68). Amram Gaon in his "Siddur"
(l.c.) calls the custom of reciting the "Kol Nidre" a foolish one
("minhag sheṭut"). According to Naṭronai, however, it was customary to
recite the formula in various lands of the Jewish dispersion, and it
is clear likewise from Amram's "Siddur" (ii. 37a) that the usage was
wide-spread as early as his time in Spain. But the geonic practise of
not reciting the "Kol Nidre" was long prevalent; it has never been
adopted in the Catalonian or in the Algerian ritual (Zunz, l.c. p.
106); and there were always many congregations in lands where the
Provençal and Spanish ritual was used which did not recite it ("Orḥot
Ḥayyim," p. 105d; comp. also RaN to Ned. 23b, where it is said: "There
are some congregations which usually recite the 'Kol Nidre' on the Day
Rabbeinu Tam states that it only effects the future and not the past.
Rabbenu Tam (1100–1171), however, disagrees, and raises many
objections to the traditional understanding of Kol Nidrei (Rosh, Yoma
8:28). He insists that Kol Nidrei does not affect the past by
annulling previous vows, but rather stipulates that any vow that one
will take in the future should not be binding. Indeed, the Talmud
(Nedarim 23b) teaches:
And he who desires that none of his vows made during the year shall be
valid, let him stand at the beginning of the year and declare, "Every
vow which I may make in the future shall be null." [His vows are then
invalid,] provided that he remembers this at the time of the vow. But
if he remembers, has he not cancelled the declaration and confirmed
the vow? ... Raba said: … Here the circumstances are, for example,
that one stipulated at the beginning of the year, but does not know in
reference to what. Now he vows. Hence, if he remembers [the
stipulation] and he declares: "I vow in accordance with my original
intention," his vow has no reality. But if he does not declare thus,
he has cancelled his stipulation and confirmed his vow.