Most Sinners are not "bad people":
"In many instances, sinners are not bad people. They have fallen into sin due to misguidance, error, or negligence."
-Imam Zaid Shakir
On seeing a Sinner:
When you see someone committing a sin, don't look down upon the sinner with pride & contempt just because you do a different type of sin (since every human being commits sins).
And don't get puffed up with self-righteousness, just thank Allah for protecting you from that sin and also for covering up your own sins! Remember, arrogance (even against a sinner) is one of the biggest sins in itself and prevents one from entering the JANNAH.
While advising a sinner (nahi 'anil munkar):
Love, real concern, softness, humility, wisdom and choosing appropriate time & place are a part of sunnah of advising & correcting others' mistakes.
Remember, a Daiee (preacher) with an arrogant (Mutakabbir) heart will never succeed in his dawah.
Imam Thanwi (R.A.) said that one should always consider the sinner, whom one is advising, to be better than oneself even at the time of giving advise. If the Daiee thinks that he is better than the sinner, he has Takabbur in his heart and hence, is a bigger sinner himself (arrogance is a bigger sin than most of the common sins)!
So, advising & correcting others is a delicate task and, if not done properly, can actually destroy your aakhirah.