Permanent Residence in the UK is called Indefinite Leave to Remain. ILR is granted to people who have already shown a commitment to the UK on a temporary visa (such as those who have successfully obtained the UK EEA Family Permit). ILR requires you to not spend 2 years or more outside of the UK, as this can lead to it being revoked.
Requirements depend on what visa they currently have and for how long. Applicants must have sufficient knowledge of the English language and life in the United Kingdom (Applicants under the age of 18 or over the age of 65 are exempt from this requirement).