When you pull up the corner of a carpet to inspect the backing/construction, you can almost always find a detached tuft or two there.
If, like me, you use multi-fibre compatible solutions, it is not always necessary to know what the fibre is, just if it's dye fast and not going to harmed by water and agitation.
Having said that, knowledge and experience means a lot and you can often make an educated guess as to the type of principle fibre, but not necessarly a blend. For example, a Brinton's Bell Twist looks totally different to a tufted twist and most other face-face wiltons. I couldn't write down what the difference is
but you can usually see it.
Safe and happy cleaning
The Ken