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how can you determine if an audio amplifier circuit is for 4 ohm or 8 ohm speaker?

most audio amplifiers are labelled "use with 8 ohm speaker" and a like.
what if there is no label? how can you determine what speaker to be used?
speaker impedance well suited for an amplifier circuit depends on what electrical component?

It will make some difference to output volume, but only really in the limit - ie maximum volume. You won't break it using 8 Ohms.

Amplifier output rating depends on the load impedance, the supply voltage and the exaxt configuration of the output stage. If you know the rated power of the amp, you can make an educated guess as you measure the output volts with a load connected, since V^2/R = power.
+1

Here's a quick rule of thumb: If it is a solid state amp made from between the mid 1970's to the present and meant for home use, 8 ohms should work. Some say 16 ohms, but they are few and far between, while others say they can go to 6, 4, 2 or even 1 ohm, but again, they are are not the norm. The only exception I can think of is Onkyo. They tend to like 6 ohm speakers and they have a habit of shutting down if you go below that.

Automotive amps tend to run around 4 ohms, with some going to 2 or 1ohm.

Tube amps tend to like higher speaker impedances with 16 ohms being the norm. Again, there are exceptions, such as guitar/instrument amps using 8 or 4 ohm speakers (some of them...).

As steveastrouk said, you need to really know the info on the particular amp in question in order to be assured you get the most power out of it safely.

Qa
. +1. Most home amps will hand 4-8 ohm speakers. Most car amps will handle 2-4 ohms. When in doubt, use higher impedance speakers - there may some loss of fidelity, but it will help protect the amp.
.  To measure the impedance of a speaker, just put an ohmmeter across the terminals.You won't actually be measuring impedance, but the reading will be close enough.