Actually it has absolutely nothing whatsoever to do with the Queen until she has to give them the medals, any UK citizen, or citizen of a Commonwealth country of which the Queen is head of state, can be considered for an Honour, provided that her/his service is to the UK or that s/he is working for the benefit of the UK overseas. Foreign nationals may be considered for Honorary Awards.
Nominations can be made by anyone but normally they come from some organisation. If you are interested you can read the process
here
Outside the UK there is a slightly different nomination process, for instance here we send a nomination to Government House rather than the Cabinet Office. We asked the Chair of our Management Committee to nominate our boss for an Honour as we felt it would be better coming from her, it took about two years before he finally received it.
As many of you won't know what happens, if a person is honoured their name is published in the press, locally and nationally. If they are not celebrities they might get quite a lot of local publicity. A couple of months after the Honours List is published (they are June and New Year) the person together with up to three guests will attend Buckingham Palace and the recipient will be congratulated by the Queen who will pin the medal on them. Obviously there is a little more to it if a person is knighted, they get dubbed with the sword!
As well as the ceremony and medal, the recipient will receive
a superb document signed by the Queen and Prince Philip, quite magnificent.
It is possible to purchase a video of the ceremony personalised in such a way as to make it look as if it was just for you, and photographs, the video is supposed to be excellent, I must borrow the boss's copy sometime.