You need a compound microscope to see most spore features but spore colour can be seen by the naked eye with the help of a spore print. It's simple to make a spore print from a mushroom:
Remove the stem by cutting it where it meets the cap.
Put the cap on a piece of paper, gills facing down.
Cover the paper and cap with a bowl or tub of some sort - to maintain the humidity around the cap.
Leave it for a few hours and then remove the tub and cap.
If all's gone well you'll see something like this:
Spore prints, pale coloured spores on a dark background (left) or darker spores on a light background (right).
Over the hours, mature spores (and only mature spores) will have been released from the gills and fallen onto the paper. What you see in a spore print, such as the one pictured, is a mass of hundreds of thousands or millions of spores. In this quantity the colour is easy to see. The commonest spore colours are white and various shades of brown.
Note that the colour of the gills need not be the same as the colour of the spores.
If your spore print is very weak (or not there) put the cap and tub back down and leave it for longer - even overnight. Some species take a long time to build up a good spore deposit.
It's also possible that the cap had already started to dry out when you collected it. Put a couple of drops of water on the cap, or a damp cotton ball next to the cap before putting the tub over. It's hard to get spore prints from mushrooms with small, thin caps. They dry out very quickly.
You can also get spore prints from the other fungi that release their spores forcibly - see SPORE DISPERSAL SECTION.
For example, you can put a section of coral fungus onto a sheet of paper, cover it and leave it for a few hours - just as you would a mushroom.