What does one say after starting prayer, cause I have noticed people muttering before reciting the Faatihah?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

There are many supplications the Prophet used to say at the start of the prayer after the first Takbeer. One of the supplications is: "Allaahumma baa'id baynee wa bayna khataayaaya kamaa baa'dta baynal-mashriqi walmaghrib, allaahumma naqqinee min khataayaaya kama yunaqqath-thawbul-abyadhu minad-danas, allaahummagh-silnee min khataayaaya bith-thalji walmaa' walbarad." (O Allaah, distance me from my sins just as You have distanced The East from The West, O Allaah, purify me of my sins as a white robe is purified of filth, O Allaah, cleanse me of my sins with snow, water, and ice).

Another one is: "Subhaanak-allaahumma wabi-hamdika wa tabaarakasmuka wa t'aala jadduka wa laa ilaaha ghyruka." (How perfect You are O Allaah, and I praise You. Blessed be Your Name, and lofty is Your Position and none has the right to be worshipped except You).

Allaah, the Glorified and the Exalted, knows best.