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

وَحَدَّثَنَا مُحَمَّدُ بْنُ عَبْدِ اللَّهِ بْنِ نُمَيْرٍ، حَدَّثَنَا أَبِي، حَدَّثَنَا هِشَامٌ، عَنْ عَبْدِ الرَّحْمَنِ، بْنِ سَعْدٍ أَنَّ عَبْدَ الرَّحْمَنِ بْنَ كَعْبِ بْنِ مَالِكٍ، - أَوْ عَبْدَ اللَّهِ بْنَ كَعْبٍ - أَخْبَرَهُ عَنْ أَبِيهِ، كَعْبٍ أَنَّهُ حَدَّثَهُمْ أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم كَانَ يَأْكُلُ بِثَلاَثِ أَصَابِعَ فَإِذَا فَرَغَ لَعِقَهَا ‏.‏