Hilchos Issurei Biah 13:5

The sacrifice brought by a convert is a burnt offering of an animal, two pigeons or two young doves. Both birds are brought as a burnt offering. Nowadays, in the absence of sacrifices, a convert merely undergoes circumcision and immersion. When the Temple is rebuilt, the sacrifice will again be required.

Hilchos Issurei Biah 13:6

If a convert is circumcised but doesn’t immerse in a mikvah, or if he immerses but isn’t circumcised, he is not yet considered a convert. A convert must immerse in front of a court of three. Since a court is required, one may not immerse on Shabbos or yom tov, or at night (when courts do not convene). However, if they had him immerse, the conversion is valid.