The first number you need to determine the doomsday for a year is to find its anchor day. Anchor days are specific to the century the date is inside.
Each century is linked with a specific anchor day, and since our calendar loops around every 400 years, there are actually only four anchor days that you need to memorise.
You must simply just memorise these weekday numbers. Luckily, in most everyday situations, dates you might want to convert to weekdays will typically be in one or two of these centuries. Knowing that years in 19xx has Wednesday as its anchor and years in 20xx has Tuesday should be enough for almost all practical use cases.