Please explain Qiyas and how do the scholars use this method to derive at Islamic rulings?

This is an area of Usul ul-Fiqh. It involves scholars giving ruling about a certain new issue not mentioned during the time of the Prophet (ﷺ). They take evidence from texts that are similiar in background with the current issue to derive at a ruling on the current issue.

As for area of Aqeedah, it is different from Fiqh as there is no new issue. Matter of belief has been established in the texts and Qiyas is not needed. The three sources for Aqeedah are Qur'an, Sunnah and Ijma' concensus of scholars from the companions.