Let's say that you want to measure the current through a resistor. In order to do that you would remove the wire from one of the ends of the resistor, place it into an ammeter and then run another wire from the ammeter to the resistor. For instance, if you had a pipe, and you wanted to measure the water flowing through it, you would have to hook up something to measure it that had the same amount of water flowing through it as the pipe. Therefore, you could replace a section of the pipe with your measuring device. If you think of the water as current, this is how ammeters work.
Voltmeters are a little different.
They measure the voltage across something. In order to measure voltage you need two points so if you wanted to measure voltage in this case, you would add a wire from each side of the resistor to the voltmeter. The voltmeter would then tell you the difference in voltage between one side of the resistor and the other. Basically, the reason that ammeters and voltmeters are connected differently in circuits is because of the differences between current and voltage.