Hi, this can get confusing because there are two different sorts of freedom. At the risk of repeating what you already know, here's a quick guide:
Usually, parents hoping that their son might work in the City would apprentice him in one of the livery companies. This would ususally be at age 14-16.
Most of livery company records have been deposited at the Guildhall (though a few remain with the original companies). A list of the Guildhall's holdings is here:
http://www.history.ac.uk/gh/livlist.htmAn apprentice would be named in the apprentice binding book of the livery company. The info here varies, but can contain: the name and occupation of the apprentice's father, the father's parish, whether the father is deceased, the name of the apprentice's master.
An apprenticeship usually lasts 7 years, after which the apprentice can become free of the company. Most companies have separate books of freedom declarations. These do not usually contain any new information, other than to confirm the completion of the apprenticeship.
Once free of the company at 21+, it is possible to apply for freedom of the City. This is a distinct organisation, membership of which entitles you to various privileges that are useful for working in the City.
These records are held by the Corporation of London Record Office, which is currently based at the LMA. They have microfilm indexes of freedom admission papers. If someone is a member, you can usually find additional documentation -- most commonly, the original indenture form from when the apprentice was 14, with a signature of the apprentice or master, and details about the progress of the apprenticeship written on the back.
If a person is called a CITIZEN is usually means he was free of the City (in addition to being free of a company).
A few of things to bear in mind:
1. The is no very close relationship between a person's livery company and the trade they take up after about 1700. The fact that someone is a grocer does not mean that they were apprenticed in the grocers company -- they could equally have been in the haberdashers company. Having said this, the company associated with the trade should be the first one to check: for printers go to the stationers company, for colourmen go to the painter stainers, etc.
2. If someone is a citizen, you should be able to find their City freedom admission papers. These will probably also tell you their livery company. You can then go back to the company papers for more information.
3. Apprenticeship and citizenship would often carry on for a few generations. A citizen would want to extend the same educational and social benefits to his children.
An example from my own family:
Henry George Johnson (1696?-1762) apprenticed his third and fourth sons: Phineas (1738-1804) as a painter stainer in 1754
Thomas (1740-?) as a wheelwright in 1755
both subsequently became free of the City in 1761 and 1762. Their indenture forms are held by the LMA.
Phineas apprenticed his first two sons
Henry George (1773-1841) as a painter stainer in 1790
James Taylor (1775?-) as a stationer
best,
Mike