Cochineal are a scale insect that feed almost solely on prickly pear cactus. These insects produce the most historically important and valuable insect dye, carminic acid. Cochineal insects contain a LOT of dye! You will get a lot of color out of a small quantity, so have fun playing with the color that it gives and have plenty of fiber on hand to play with! 

Cochineal produces very wash and lightfast reds, pinks and even lavenders. Cochineal can be dyed on wool as an acid dye, with the use of tannin and acid instead of a mordant, as has been done historically, but is most often dyed with a mordant such as Alum.   Both work well and are lightfast.  A mordant is needed to dye cellulose fibers with cochineal.

Cochineal is very pH sensitive. The presence of acid will shift the color towards red, while an alkaline pH will move the color toward purple. 

A true scarlet can be achieved by using tin as a pre-mordant or by adding a small amount of tin (3%) and cream of tartar (6%) to the dye bath. 

The color can be shifted toward purple with ammonia or soda ash as a post-dye alkaline pH adjuster, but a more stable purple color results from using a very small amount of iron (less than 1%) as a post-dye bath.

Over-dyeing Cochineal with Woad produces beautiful purples and over-dyeing cochineal with madder produces a true red.

Cochineal is not sensitive to boiling, so you don’t need to worry about water temperature when dyeing.  Make sure to wash your yarn in a neutral detergent after dyeing, so that you do not inadvertently change the color because of pH changes from detergent.  Original blue Dawn is said to be pH neutral.

It is often recommended to soak cochineal over night before dyeing or simmer and strain before dyeing fibers.  I often like to put my fibers right in the pot with the dye stuffs.  The drawback to this with cochineal is that you will end up with dark pink or red spots on your fibers or cloth where the cochineal has laid on the fiber. 

Use alum mordant at 15% WOF (weight of fiber) for protein fibers such as wool and silk. For cellulose fibers mordant with tannin at 8% WOF and then alum at 15%, or alum acetate at 8%. If you use cream of tartar (tartaric acid) at 6% WOF and add it to the alum mordanting bath or the dyebath, the color achieved will be more red. 

I have read that the famous British red coats were dyed with Madder and Cochineal. If what I have read and remember is true, the standard issue coats were dyed red with Madder, which gives a more orang-ish red. Officers would pay to have their coats dyed with Cochineal which gives a bright more blue-ish, true scarlet red color.