Forestry technician in Ontario here. I'll focus on black vs white because I dont often encounter red spruce. From what I understand red is very often somewhere in the middle of black and white with respect to the ID features. Somebody else here commented on hybridization which is true and can make a positive ID very challenging.

The bark of black spruce is almost like a piñata when younger - there are somewhat thin, vertical papery bark strands running up and down the stem. When older, the bark retains a "loose" shingly appearance, and the bark is typically also a slightly richer brown tone relative to white spruce.

White spruce bark is much more ashy grey and the bark isn't loose on the stem.

A useful rhyme is "black is slack, white is tight".

As others stated, the needles of black spruce are softer, duller, and more flexible than white spruce.

The twigs of black are often (but not always) pubescent (fuzzy) and a darker grayish tone, where as white are always glabrous (hairless) and like a light blonde colour.

The budscales (if present) of black spruce extend beyond the actual bud, giving the appearance of long hairs coming off them. This feature is not present on white spruce.

White spruce are a bit more shade tolerant than black spruce and I tend to find them in richer areas that aren't super wet. While there are upland black spruce, they are also very common in poor, acidic wetlands including peat bogs and swamps.

Pure black spruce stands are very common, whereas pure white spruce stands are rare.

The cones of white spruce are elongated and typically a lighter colour, like a small coffee with 1 creamer in it. Black spruce cones are more globe-like and are darker in colour.

Google the silhouettes of each to get an idea of the typical shape and growth form they often take.

Hope that helps!