It is recommended to lick one's fingers and wipe the bowl, and to eat a piece of food that is dropped after removing any dirt on it. It is disliked to wipe one's hand before licking it, because of the possibility that the blessing of the food may be in that remaining part. The Sunnah is to eat with three fingers

حَدَّثَنَا مُحَمَّدُ بْنُ عَبْدِ اللَّهِ بْنِ نُمَيْرٍ، حَدَّثَنَا أَبِي، حَدَّثَنَا سُفْيَانُ، عَنْ أَبِي الزُّبَيْرِ، عَنْ جَابِرٍ، قَالَ قَالَ رَسُولُ اللَّهِ صلى الله عليه وسلم ‏ "‏ إِذَا وَقَعَتْ لُقْمَةُ أَحَدِكُمْ فَلْيَأْخُذْهَا فَلْيُمِطْ مَا كَانَ بِهَا مِنْ أَذًى وَلْيَأْكُلْهَا وَلاَ يَدَعْهَا لِلشَّيْطَانِ وَلاَ يَمْسَحْ يَدَهُ بِالْمِنْدِيلِ حَتَّى يَلْعَقَ أَصَابِعَهُ فَإِنَّهُ لاَ يَدْرِي فِي أَىِّ طَعَامِهِ الْبَرَكَةُ ‏"‏ ‏.‏