General approach
The records and approach to researching a man of the artillery is no different to that of a man who served, for example, in the infantry or cavalry. The men’s service records, campaign medal records, gallantry and bravery awards, casualty lists, records of death, etc are all in the same collections.
See my pages How to research a soldier and A Soldier’s life for full details.
Records specific to the artillery
Online
Original enlistment books owned by The Royal Artillery Historical Trust and housed at The Royal Artillery Museum have been digitised and can be found online only via Findmypast.
They have called this record set Royal Artillery Attestations 1883-1942. The books list around 1 million men but not all soldiers who joined the artillery are included.
Not all of the columns were always completed, but an entry in this book can be most valuable. In particular, even though the entries were for post-Great War attestations, that they can provide Great War data is be of significance in your search.
The online service Findmypast also has a searchable copy of a regimental number register from the Honourable Artillery Company Archive. It can be a useful document, for it often includes not only the man’s name, rank and numbers but private addresses and fragmentary details of service history. The register includes men who served with 309th (HAC) Siege Battery of the RGA.
Print and physical copy
The Royal Artillery Museum, the National Army Museum, the Imperial War Museum and the Liddle Collection at the University of Leeds all have holdings that cover various aspects of the men and units of the Royal Garrison Artillery, but unless you are exceptionally lucky you are not likely to find your man mentioned by name.