The fibres from plants are extracted from the rest of the plant material. They are then mixed up into a tangle and flattened into thin sheets. All this is sounds easy, but requires a lot of knowledge and skill. The process involves several distinct stages. I was booked for a paper-making course during 2020 ~ history will remind you as to why that was not possible. So this description is a bit of a make-up. Please drop me a note if I am wrong in any detail. I write as if they are 'instructions' ~ but do not take my word for anything.
Choose suitable plants ~ grass ~ flax ~ cotton ~ hemp ~ bamboo ~ and treat them to reduce them to as fine a set of fibres as possible. Alternatively find some pure cotto or linen ~ pure means 100% ~ man-made fibres will spoil things. This will involve a lot of physical effort ~ beating ~ crushing ~ pummelling ~ bashing.
Mix the fibres with water ~ and maybe other additives ~ such as aquapel ~ to control eventual water-permeability ~ size and tub-sizing ~ and clean the fibres, removing impurities ~ until a furnish of the right consistency is obtained. Only experience will defineright consistency ~ and it all depends on the planned final use.
Using a large flat seive ~ a deckle ~ scoop-up a puddle of furnish.
Spread the furnish evenly over the mesh of the deckle, ensuring the fibres are well entwined. This shaking is where a great deal of skill is required to obtain a strong paper.
The amount of furnish in the deckle will determine the finished weight of the paper.
Lift up the seive and drain much of the water through it.
Once the mass of fibres has firmed up ~ maybe in a matter of seconds ~ remove the sheet, carefully, and gently lay it onto a blanket ~ couching.
Cover the sheet with another blanket.
Scoop up another deckle-full of fibres, and repeat many times, building up a pile of paper-blanket-sandwiches. In a mill this pile could be a metre high.
Press the pile of blankets and paper sheets. A lot of pressure is required. A hydraulic pump ~ such as a car jack ~ is used for this.
As the excess moisture is squeezed out of the pile the weave of the blanket leaves a smooth or rough impression on the paper. The final surface of the paper is determined by the roughness of the blanket. If smooth hot rollers are used the surface will be called Hot Pressed. If no smooth rollers are used then it is Cold Pressed or for short NOT pressed. The word pressed is left out,and the word NOT fully captialized in order to distinguish it from the normal use of the word 'not'. The use of heated rollers, I presume, takes the process away from the realm of being Hand Made
Depending on the final use another sizing maybe required. This is done by dipping the papers in a gelatin bath or some such specialist ~ maybe secret ~ treatment.
The paper is now ready to dry. Hanging up in a gentle airflow is best ~ air drying ~ on a clothes-line arrangement.
When dry the paper is ready for use. The surface will remain rather too rough for office use, but with care it may be smooth enough for pen and ink. Artist's find it suits their needs for watercolour and other media, especially if the sizing processes treat the surface to better accept their paints. One artist I know will only use one particular brand of hand-made paper because he like its characteristics ~ which suit his style.
Sometimes petals can be added to the mix.
Machine-made papers use all the same processes ~ but on a continuous belt. The paper comes out at the finishing end as wide as a road ~ and at speeds comparable with fast cyclists or slow cars. China clay and resins may be added to improve the surface ~ together with numerous rollings and hot pressing.
I look forward to adding some pictures to explain all this better than any words can.
Two Rivers papers are handmade in Devon 
Khadi papers are handmade in India 
Lokta papers are handmade in Nepal