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 Sahih Muslim 2033 f

Arabic hadith text
وَحَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، حَدَّثَنَا مُحَمَّدُ بْنُ فُضَيْلٍ، عَنِ الأَعْمَشِ، عَنْ أَبِي، صَالِحٍ وَأَبِي سُفْيَانَ عَنْ جَابِرٍ، عَنِ النَّبِيِّ صلى الله عليه وسلم فِي ذِكْرِ اللَّعْقِ ‏.‏ وَعَنْ أَبِي سُفْيَانَ عَنْ جَابِرٍ عَنِ النَّبِيِّ صلى الله عليه وسلم وَذَكَرَ اللُّقْمَةَ نَحْوَ حَدِيثِهِمَا
Translation

Jabir reported from Allah's Messenger. (ﷺ) about mentioning the licking (of fingers) and the (falling of) the mouthful.