The procedure is dealt with in Mishna Pesachim 5 (5, 6 & 7).
5) The Pesach sacrifice was slaughtered in three groups, as it is
stated (Exodus 12:6), "The whole assembly of the congregation of
Israel shall slaughter it," [i.e. three groups according to the three
different terms used to refer to the Jews:] assembly, congregation,
and Israel. The first group entered, [until] the [Temple] courtyard
was filled, [and then] the gates of the courtyard were closed. [And
then] Tekiah [a long uninterrupted call], Teruah [a long staccato
call] and Tekiah were sounded. The Kohanim [members of the priestly
caste, a subgroup of tribe of Levi, which is uniquely responsible for
maintaining and carrying out the sacrificial services in the Temple]
would stand in double rows and in their hands were beakers of silver
and beakers of gold, [namely] one row which was completely silver, and
one row which was completely gold; they would not mix [them]. And
there were no [flat] bottoms to the beakers, lest they would put them
down, and the blood coagulate.
6) A [common] Israelite slaughtered [the Pesach sacrifice], and a
Kohen received [the blood] and gave it to his fellow [Kohen], and his
fellow to his fellow; and [each] received a full [beaker], and [at the
same time] returned an empty [one]; the Kohen nearest to the altar,
sprinkled it out in one sprinkling at the base [of the altar].
7) When the first group went out, the second group entered; when the
second went out, the third entered. Like [the proceedings] of the
first [group], so [too] were [the proceedings] of the second and third
[groups. Each group] would [also] read the Hallel [Psalms of
thanksgiving recited joyously and communally on many festivals]: if
they finished [it], they would repeat [it], and if they repeated [it
to its end], they would read it a third time; even though, during all
their days, they never read it a third time; Rabbi Yehuda says,
"During all the days of the third group, they never got [as far as]
'ahavti ki yishma Hashem,' because [that group's composition] was
That was in the time of the mishna. When the Temple is rebuilt (speedily in our days), we might expect that there will be many more people!
Roasting and eating could be in the whole of Jerusalem.