You just get used to it after a while. Your shins become better conditioned, mentally you're used to the pain and it doesn't bother you so much.
From my experience, it depends on what technique you're throwing. The hardest part of your shin is just under your knee, and ideally that is the best part to use, but it isn't always practical. For example, with a body kick, if you land with the top of your shin, you will often be in Boxing range and can get countered very easily. The center to the bottom of the shin is usually what I land with when throwing body kicks, and for low kicks I try to land with the top. Head kicks, you can get away with landing with your foot, but it's not a great habit to have since you can break it so easily compared to the shin.
The front of the shin is best. It digs deeper and is more stable.
Bas Rutten has a good video about it. From my personal experience, outside of it being more structurally sound to the land with the front, if you land with the side of the shin you can sometimes slam your calf into your opponent's check. Happened to me once and my calf was dead for a few rounds.