Hold the LP up to a bright light and look closely at the end-groove area on either side. The matrix number will be etched in either a formal typeface or simply a handwritten scrawl. Use a pencil to write down the exact code on a piece of paper.
Hold the other side of the LP up to a bright light and write down the number that appears on that side.
Compare the two numbers you have recorded. Matrix numbers are always different on each side of the LP, though the difference is often slight. For example, the A-Side might read "SRM-1-605-M2" and the B-Side might read "SRM-1-605B-M2." If the numbers match, check again to be certain you have not mistakenly recorded the catalog number on the label rather than the matrix number.
Identify the record label that issued the recording. That information will almost always appear on the record jacket and usually on the LP label as well. Different companies had different systems for generating matrix numbers. For example, RCA uses a letter as the first character in the code which indicates the year a record was mastered. Though you can quickly find online information about popular LPs like Beatles records, more obscure labels might require additional research and inquiries, both online and offline. Do not be afraid to contact your local used record store. They might save you a lot of work.