Most airports of the world have one or more international transit areas which are completely separated from domestic flights, and in which passengers connecting via that airport from and to other countries do not need to pass immigration and formally enter that country. If your flights are on a single booking, then your checked baggage will be transferred for you and you will not go through an immigration check. In many airports you will still go through a security check between arrival and departure, or at the departure gate.
The exceptions to this are widely known: The USA requires all arriving passengers to formally enter the country and pass immigration and customs before connecting to their onward flight. Canada requires the same, except for onward flights departing to the USA on the same calendar day (and they are slowly moving toward full sterile transit as is done in the rest of the world). Dublin Airport is a lesser known exception with no sterile transit area, but in practice this only involves an immigration check and does not require re-checking baggage. The Schengen area is another well known area in which some 26 countries share a single external immigration border.
If you fly on separately booked tickets, this is called a self-connection, and in this case you almost always have to pass through immigration and customs and transfer your checked baggage yourself to your onward flight. The only exception I know of to this is at Dubai (DXB), where there is a paid service available at the airport which will transfer your baggage and check it in to your onward flight when you've booked separate tickets.
For your flights, you won't do anything in Amsterdam or Paris except go directly to your connecting flight by following the flight connections signage to your departure gate.