How can I tell if a fabric is 100% cotton

One should not be sure without certain testing physical and chemical testing. Because many cellulosic fibres possessing behavior like cotton. And there are many variants of regenerated cellulosic fibers that demonstrate properties similar to cotton. Even spun polyester is being sold on the name of cotton and also there are blended fabrics.

Fabric is a hundred percent cotton or made of something else is a concurrence of many observations.

Visual: Staple fibers are indicators of natural fibres, The microscopic view of different textile fibre is the primary point of observation. The twisted ribbon-like structure informs the cotton.
The tactile sensation: Cotton is very comforting to the skin, the feel is not wet and slippery. Its touch is dry and feels soft, fluffy and absorbent.

Multifunctionality: Although cotton is good for hot weather, it wicks the moisture and feels cool in summers but one can not ignore cotton in winters, it feels warm and cozy in the winter. Cotton as inner layers feels good.

Absorbency: Waterdrop will be absorbed immediately until unless it is treated with hydrophobic chemistry.

Burning test: If it is exposed to the burning test, it will burn with a smell like burning paper and soft ash of black/grey will be residue. And and majority of synthetics such as polyester and Nylon will burn like plastic and the residue will be a hard beed.

Chemical test: Cotton dissolves in a 70% sulphuric acid solution. It is robust to harsh alkaline treatments.

Moisture regain: Dry sample of cotton will regain a moisture up to 8%