The CEFR (Common Framework of Reference for Languages) identifies six levels of language proficiency, from the lowest to the highest: A1, A2, B1, B2, C1, C2.
In order to apply for a long-term residence permit, it is necessary to have A2-level Italian language certification, while B1-level certification is required to obtain Italian citizenship.
Information on the long-term residence permit: https://www.interno.gov.it/it/temi/immigrazione-e-asilo/modalita-dingresso/test-conoscenza-lingua-italiana
Information on the application for Italian citizenship:
Locations where to take the CILS exams in Lombardy: https://cils.unistrasi.it/179/56/Lombardia.htm
Cgil Monza e Brianza offers assistance in all citizenship matters through the Cgil migrant office and patronato Inca in Monza and Brianza, including the request and booking of the Italian Language Test.
This link provides contact information for the migrants' office: https://www.cgilbrianza.it/area-migranti-e-politiche-sociali/. Two new offices have recently been opened in Limbiate (Spi Cgil headquarters in Piazza Aldo Moro) and Cesano Maderno (Camera del Lavoro, Corso Libertà, 70). Here is all the information: https://www.cgilbrianza.it/sportello-migranti-nuove-aperture-in-brianza/