LSAT is not a computer based test.
LSAC has not announced any plans to turn the LSAT into a computer-based test (CBT) or a computer adaptive test (CAT).

The LSAT has five multiple-choice sections.
Each lasts 35 minutes.
Only four of the sections are counted toward your final score.
The unscored "experimental" section is used to try out questions for future tests.

These are the sections:

2 Logical Reasoning sections ("Arguments" or "LR")
1 Analytical Reasoning section ("Games" or "AR")
1 Reading Comprehension section ("RC")
1 Experimental section (this could be LR, AR, or RC)

These five sections can appear in any order.
There is no way to tell which section is experimental, so you have to try hard on all of them.

A 35-minute writing sample is administered at the end of the test.
The writing sample is not scored by LSAC, but copies are sent to all law schools to which you apply.