Carpets can be made with natural or chemical dyes. With wool on wool and wool on cotton carpets, natural dyes are preferable. Natural dyes do not bleed when it gets wet and when you wash the carpet. This can be very important, especially when you are buying a carpet with white in it, because other colours will bleed into the white and make it look very ugly. There are a couple tests that you can do on the carpet to test whether they use chemical or natural dyes. The first is to have a fairly damp white cloth and rub it against the carpet. If the colour is natural dye then only fibres will come out, and that will be the only colour that leaves the carpet, while if chemical dyes are used, colour will actually bleed into the whiteness of the cloth, as well as little pieces of wool coming off. Natural dyes are more expensive than chemical ones and the price of the carpet will thus be higher. Remember to do this test on each colour of the rug, especially if you are doubting the authenticity of the natural dyes, because its possible that some colours in the rug are natural, others chemical.
Another way to tell if a carpet is natural or chemical dyes, is how it fades. This is especially noticeable if the carpet has been out in the sun for any extended periods of time. You open up the carpet to see the bottom of the thread, often by bending the carpet in half, or just opening it up with your fingers. If the thread near the bottom of the knot is a different shade of colour than the top of the thread, it is a chemical dye.
Silk carpets are almost always made chemical dyes.
Dead or live wool
Dead wool is cut after the sheep has died, and the wool is harsh and rough because it has lost its natural oils. Live wool is sheared when the sheep is alive, and retains the natural oils. Most Turkish Carpets are made of live wool because it is finer and not as rough.
Handspun or machine spun weave
This is only applicable to wool on wool carpets. Machine spun wool is much tighter spun than handspun, one would think this is a good thing but because its much tighter, and wool is not very strong, many of the wool fibres snap while they do this, which limits the lifetime of the carpet. Handspun increases the hours of labour and the price accordingly, but it is not spun as tightly as machine spun so the lifetime of the carpet is longer. Now how to tell whether your rug is handspun or machine spun. The only way to do this is to flip the carpet over and look at the weave. If all the little squares are exactly the same size, then its machine spun. If there are size differences in the squares then it is handspun. It is very difficult to find handspun carpets, especially in the big cities.