Judaism is not divided on the issue.
The details of the Passover practice are very very clear and available.
We've been doing the process every year from the last night we spent in Egypt.
When we were no longer able to sacrifice, we replaced it with study of the process.
The sacrifice was done on the eve of the Passover -- in the afternoon of the 14th.
It is eaten on the Seder - on that same evening (which, by Jewish reconing is the 15th)
Karaite Judaism was a splinter group that began a few hundred years after the destruction of the temple
Without getting into detailed Jewish scholarly materials,
you can get a good feel for what the Seder (the festival meal) was like in the Roman period from the stories in the Haggadah (the pamphlet for running the Seder in the post-Temple era).
Bottom line --
discuss at length the redemption from Egyptian exile
eat a wrap of soft Matzah, with lamb (the sacrifice), and lettuce
have four cups of wine
For answers to questions regarding Jewish practice -
try
www.chabad.org
for articles and literature
or
www.askmoses.com for online chats and email
There is a group focused on setting up the temple and bringing the sacrifices
They hold an educational "practice Passover sacrifice" every year about a week before Passover on a mountain overlooking the Temple.
The Temple Institute
http://www.templeinstitute.org/
You can also look on the Hadassah magazine archives for a wonderful photo essay of the Samaritan Passover sacrifce.
Note - when asking questions on Jewish forums, it is more effective to ask "in the Roman occupation period"
rather than "at the time of Jesus" seeing as Jews are kinda iffy on the whole Jesus thing.