Multiple Passport Issues

Could anyone who has multiple passports (either from different countries or from the same country) advise me if it is possible to enter a country using one of the two passports and then leave using the other one. For example, if you send the passport which has your entry stamp to some other foreign embassy to get a visa, are you unable to use the other one to travel somewhere else before your first passport is returned?

If not, when you arrive at the next country, do they check to see if you have a valid exit stamp from the country you just left? Does it matter whether you arrive by land or by air?

The thing which I am wondering about is how do you get your second passport into the flow of things.

Thanks to anyone who has any experience with these matters.