Is it possible for someone to have faith in Jesus without repenting of their sins? If so, how does one go about repenting of their sins the biblical way?
The Greek word translated repent in the New Testament means to change one’s mind. In connection with salvation it refers to the time when unbelievers change their mind and admit they are sinners. This leads to the recognition that they need a Savior and results in them asking Jesus into their heart.
Therefore, when a person comes to believe in Jesus for their salvation they have already repented.
If you are talking about people changing their behavior after they are saved, you mean regeneration. Regeneration is the process where a believer heeds the conviction of the Holy Spirit and begins progressively discarding old ways that are not pleasing to the Lord and adopting different behavior that is more pleasing to Him. They do this as an expression of their gratitude for the free gift of salvation. This is the Biblical way of changing our behavior. It is outlined in Romans 12:1-2 and explained in greater detail in Ephes 4:22-32.
Many believers do not allow all of the regeneration process to take place, but that does not take away from their faith in Jesus to save them. Our salvation is based on what we believe, not on how we behave, and was guaranteed from the time we became a believer (Ephes 1:13-14).