I know the New Forest well, I used to live in Ringwood.
To become a commoner you essentially have to buy some land that comes with the right to common on the new forest.
Commoners are those who occupy land or property to which privileges
known as ‘rights of common’ are attached, which includes the right to
graze stock on the Open Forest.
Given that the New Forest is one of the most expensive places to live in the UK, this doesn't come cheap. A house with common land privileges in the New Forest is likely going to come with a price tag in the millions of pounds. There is a problem with commoners not using their right to common. It's become a status symbol to be "a commoner", but the London bankers who buy these kinds of properties rarely have any interest in the upkeep of the traditions.
For those that are interested in what a commoner is, it is basically someone who has the right to gaze sheep, horses, cattle in the New Forest boundary. It was an institution created by William the Conquerer in the 11th Century.
See Commoners of the New Forest