I previously wrote about what it means to assent based on faith, relying partly on a quote from Cardinal Newman. I also posted on whether doubt and faith are compatible, in other words, once you have decided to place your faith in a source of information, can you simultaneously continue not placing your faith in that source?
Here is some more Cardinal Newman on what it means to assent based on faith:
From the time that I became a Catholic, of course I have no further history of my religious opinions to narrate. In saying this, I do not mean to say that my mind has been idle, or that I have given up thinking on theological subjects; but that I have had no variations to record, and have had no anxiety of heart whatever. I have been in perfect peace and contentment; I never have had one doubt. I was not conscious to myself, on my conversion, of any change, intellectual or moral, wrought in my mind. I was not conscious of firmer faith in the fundamental truths of Revelation, or of more self-command; I had not more fervour; but it was like coming into port after a rough sea; and my happiness on that score remains to this day without interruption.
John Henry Newman, Apologia pro Vita Sua, p. 238.