Generally speaking - you go into the yard, pay the guy a dollar (or 3), sign a disclaimer (basically saying that you read the rules). Go in and walk around to find your car. You bring your own tools, there may or may not be a sink or some laundry detergent or goop available to wash up.
You work on the donor car, pull the part you need, bring it up to the counter and purchase the part. On the "working" parts, (a/c compressors, fans, radiators, etc) they often offer a few dollar warranty. This means that if the radiator has a hole - you can come back and pull another. Prices are dirt cheap. Example - Radiator is $30 in the yards, $110 new. Alternator is $45 in the yards $150 new.
Almost universally (in FL) yards will tell you what cars they have or publish them online or on a map or at minimum separate the cars out domestic vs import and split the cars up by manufacaturer. Thus all the chevys are in one row, all the pontiacs in the next, all the fords in the next, etc. Some don't do this, some won't even tell you whats in the yard and will tell you to come on down. When i was in Detroit at the yards out west, they didn't do any of that and just threw the cars in the next available slot.
Note: My wife drives a 2001 PT Cruiser, and just recently (past year) have I found any worthwhile in the yards. In fact I went all of last year without finding one in the huge yard, and only in march found 3x pt's at a yard, they were stripped by the end of the week. If your car has a "0" in the year, it probably won't be there. Typically cars are repaired until about 10 years out, and then they start getting totalled. So what year is your mazda3? I'll admit I haven't looked but I suspect if its a 05+ there is almost no way you'll find one unless its been in a terrible accident.