IT IS MUSTAḤABB, when putting on clothes, shoes, trousers and the like, to begin with the right sleeve or the right leg or foot. One should take off the left [part of the garment] first and then the right. The same applies when putting on kohl, using a toothstick (siwāk), cutting the nails, trimming the moustache, plucking the armpits, shaving the head, greeting in ṣalāh, entering the mosque, coming out of the lavatory, doing wuḍū’, bathing, eating and drinking, shaking hands, kissing the Black Stone, taking something from someone or giving it to someone, and so on. All these things should be done with the right. Their opposites should be done with the left.
We relate in the Ṣaḥīḥs of al-Bukhārī and Abū al-Ḥusayn Muslim ibn al-Ḥajjāj ibn Muslim al-Qushayrī an-Naysābūrī that ‘Ā’ishah 
said: “The Messenger of Allah 
liked to begin with the right side in all that he did—in his ablution, combing his hair and putting on shoes.” [1].
said: “The Messenger of Allah liked to begin with the right side in all that he did—in his ablution, combing his hair and putting on shoes.” [1].We relate in the Sunan of Abū Dāwūd that ‘Ā’ishah said that the right hand of the Messenger of Allah was used for his ablution and eating and drinking, and his left hand was used for the lavatory and for anything harmful. [2].
said that the right hand of the Messenger of Allah was used for his ablution and eating and drinking, and his left hand was used for the lavatory and for anything harmful. [2].We relate in the Sunan of Abū Dāwūd and the Sunan of al-Bayhaqī that Ḥafṣah said that the Messenger of Allah would use his right hand for eating, drinking and putting on clothes, and his left hand for other things. [3].
said that the Messenger of Allah would use his right hand for eating, drinking and putting on clothes, and his left hand for other things. [3].We relate in Abū Hurayrah 
who reported that the Messenger of Allah said: “When you put on clothes or make ablution, start with your right.” [4].The hadith is ḥasan, according to Abū Dāwūd, at-Tirmidhī, Abū ‘Abdullāh Muḥammad ibn Yazīd, Ibn Mājah and Abū Bakr Aḥmad ibn al-Ḥusayn al-Bayhaqī.
who reported that the Messenger of Allah said: “When you put on clothes or make ablution, start with your right.” [4].The hadith is ḥasan, according to Abū Dāwūd, at-Tirmidhī, Abū ‘Abdullāh Muḥammad ibn Yazīd, Ibn Mājah and Abū Bakr Aḥmad ibn al-Ḥusayn al-Bayhaqī.There are many other narrations on the same subject. And Allah knows best.
References
[1] Al-Bukhārī (168) and Muslim (268).
[2] Abū Dāwūd (33). Ibn Ḥajar grades it as ḥasan.
[3] Abū Dāwūd (32) and al-Bayhaqī (1/86).
[4] Abū Dāwūd (4141), Ibn Mājah (402), al-Bayhaqī (1/86), and at-Tirmidhī (1766), who states that this hadith is ḥasan ṣaḥīḥ. Ibn Ḥajar grades it as ṣaḥīḥ gharīb.