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HumanEarth there's more than one way but for me being someone at the very bottom end of the scale here's how I do it....
I'm in the UK too so bear that in mind....
I joined PRS (Performing Rights Society) many years ago. You agree for PRS to gather and distribute your royalties in your behalf. Essentially allowing them to take a small cut.
Having done that you then register any new work with them. You give them the title, whether anyone else contributed and the proportion of royalty and how to spit between the writers.
You also give them information on where it might be used ie streamed or broadcast etc.
Each work is given a unique code. You then can link that to the work.
PRS then gather data and determine royalty amounts etc. 4 times a year they distribute the royalties.
If you do live gigs you tell them where and what played. That was my old route of income essentially play live gigs, report what I played and in turn later get the royalty due from the venue to me for having my music played in their venue. But today it was because of online streaming plays.