When you put on clothes and when you perform ablution, you should begin with your right side
Authentic hadithعن أبي هريرة رضي الله عنه مرفوعًا: «إِذَا لَبِسْتُم، وَإِذَا تَوَضَّأتُم، فَابْدَأُوا بَأَيَامِنُكُم».
Abu Hurayrah (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) said: "When you put on clothes and when you perform ablution, you should begin with your right side."
Explanation
This Hadīth affirms the desirability of beginning with the right side in all good things. So, the Prophet (may Allah's peace and blessings be upon him) exhorts us to start from the right side when we wear our clothes or when we perform ablution. An exception are some organs included in the ablution, namely the two ears, the two palms, and the two cheeks. Each of those pairs is to be washed at the same time, if possible; otherwise, we should begind with the right one.
Source · Narrated by Ibn Majah - Narrated by At-Termedhy - Narrated by Abu Daoud - Narrated by Ahmad
From the Hadith Encyclopedia (hadeethenc.com).