The proper way of doing Tayammum is when someone is in need of making either ghusl or wudu and has no water and is convinced that he can reach it then he can do it. also, if someone is afraid of increasing ailment then he can do it. Or when someone has just enough water that it’s enough for drinking or wudu then Tayammum is fine. Or one has water but no ability to use it then it’s also fine to do Tayammum.
In conclusion, one would do Tayammum because of some excuse or lack of water.
The way to do it is make an intention, then place your hands on pure clay and move them back and forth a little bit, it can be anything related to earth, like rocks, or sand, whether it has dust on it or not. Then one should jerk the hands a little bit from the corners without dusting off just to remove any filth or junk. Then one should wipe the face with the hands completely without leaving any spot on it. Then put the hands on the clay again like last time and this time wipe both hands including elbows. Whatever you have to wash in wudu must also be wiped in Tayammum and there are only two times that we put our hands on the object of Tayammum.