Throughout my readings about fungal polysaccharide extraction methods, the most popular one was boiling water extraction, performed after you defat and deproteinize your initial powder. Basically you dry your matrix, grind it to achieve small sieved particles, use one of the many different methods for removal of proteins and fats (such as Sevag and others), resuspend the pure material to water and set to boil (80 to 95°C). After some time, you filter it, add absolute ethanol to a ratio of the filtrate, and the precipitate is your polysaccharide-rich sample.
To confirm its structure some basic procedures such as sugar composition (e.g HPAEC-PAD) and molecular distribution (HPSEC-RID or HP-GPC) are usually standard. NMR and FT-IR are great spectroscopic tools to help you even further characterize it. If you are interested in oligosaccharides, you will need to fractionate your samples through other techniques, and maybe evaluate it through HILIC or other methods.