Your first port of call to take on an allotment plot would be to contact your local authority; Your local Parish/Town/Borough/City Council who may run your local allotment sites or be able to provide contact details for private allotment societies in your area. This varies from area to area and availability can be limited with long waiting lists.
If you find that there is no allotment site in your local area, you can apply to your local authority under Section 23 of the 1908 Small Holdings and Allotments Act whereby all local authorities have a mandatory obligation to provide allotment provision excluding London (London Government Act 1963). This can be a long process and you will be required to bring together at least five other local council tax-payers who would also like an allotment plot to write an official letter requesting this provision.
If you have local knowledge of nearby land; particularly disused land, it would be worthwhile to find out who owns the land and approach them. Many keen growers are transforming their own gardens into kitchen gardens and vegetable patches to be able to grow their own.
There is also the option of joining a Community Garden, however that option negates the opportunity to independently grow and lay out your plot as you desire.
An allotment society will usually be run by an elected committee who will collectively make decisions on funding, equipment and works to be carried out on site and any actions to be taken. They will invite members to an annual AGM meeting where plot holders will have the opportunity to vote in committee members and voice any concerns about the allotment site.
Committee members can sometimes claim work hours and some members will be voluntary, but they will have their own individual roles and skill sets to offer; such as treasury, chairperson and so on. Many committees will offer above and beyond the requirements and have more facilities for their plot holders and may also run a shop for growing essentials.
Many committees become members of the National Allotment Society and such organisations to ensure good practices and legal compliance for their allotment sites.
Once you have applied and have been offered a plot, you will be issued with a legal document to sign called an Allotment Letting Agreement; a Tenancy Agreement. The tenancy agreement sets out the rights and responsibilities of the plot holder. Common clauses include rent, duration of the lease and termination notice, undertakings of the allotment holder as well as permitted activities, the building of structures and sub-letting rules.