Work in a fixed sequence: standard mark first, office second, date letter third, sponsor's mark last. The standard mark (lion passant for sterling silver, the crown-and-carat or numerical marks for gold) tells you the metal and legal fineness, which constrains everything else.
The assay office mark (anchor for Birmingham, leopard's head for London, and so on) tells you where the case was tested. This matters because each office ran its own date-letter cycle and typeface, so the same letter means different years at different offices.
The date letter is read against the published cycle for that office, matching not just the letter but its shield shape and typeface — the cycles repeat roughly every twenty to twenty-six years, and the shield style is what disambiguates which cycle you are in. Published tables (Bradbury's is the standard reference for British marks) exist for exactly this purpose.
The sponsor's mark — the registered initials of the firm that submitted the case — identifies the case maker or importer, not the movement maker. For imported watches, special import marks apply, and their presence can indicate that the case was assayed on arrival rather than at origin.
Record all four marks, photograph them clearly, and state the date as the hallmark gives it: a case assayed in 1915 proves the case existed in 1915, and strongly suggests the watch was cased near then, but it does not by itself date the movement — movements and cases could be paired later, and honest cataloguing says so.