The base-level answer is quite easy. Verses like Ephesians 2:8-9 make it clear that we're saved by faith in God's grace, rather than trying to justify ourselves to God through our deeply-flawed works. But Ephesians 2:10 follows by noting that we're created to do good works. We're not saved by "good works". But we're saved-- and then we're supposed to do good works from the overflow of a saving faith and the empowerment of Christ in us. Or in a word, we're not saved by good works, but to do good works.
Biblically, there is (or can be)
some challenge here. The biggest rub is not (and cannot be) the existence
of sin or even "besetting sins" (however defined), since everyone
sins, believer or not.
Particularly from John's epistles
and James, the question is what to infer from a lack of fruit or the production
of largely-rancid fruit. The problems are that:
a.) it's difficult for one to judge
someone else on this (in fact, there are warnings against that and prohibitions
against a firmly-held sense of judgment about someone else); and
b.) it can even be difficult to
judge that within oneself-- thus, leading to potential and highly-appropriate
questions about whether one has a saving faith.
If I had to recommend one passage on
this, it'd be James 2 on "can such faith save?". There, Abraham and
Rahab are examples of those who are justified before people by their deeds,
even though they are justified before God by their faith. John and James indicate/write
that if I don't have appropriate fruit in my life, then I (and those close to
me) should be asking some tough questions.
If one is saved by grace, embraced
through faith-- and has the relevant "fruit"-- then biblically, one
can be assured of salvation, eternal life, Heaven, etc. It requires as much
faith as believing that Abraham Lincoln was president.