Use REGEXREPLACE or SUBSTITUTE to replace the letters by numbers, then SPLIT to separate the values into an array of values and put that inside the formula that will use that values to do something.
If you didn't do this yet, look for the description of each function on https://support.google.com/docs or the list of functions on the Help menu from Google Sheets.
Let say that we put the letters in A1:A3, then the corresponding values in B1:B3.
With a separator (in this case coma)
The value A,B,C
to be converted is in C1.
Using SPLIT
=ArrayFormula(SUM(IFERROR(VALUE(SUBSTITUTE(SPLIT(C1,","),A1:A3,B1:B3)),0)))
Using regular expressions
=ArrayFormula(SUM(IFERROR(VALUE(SUBSTITUTE(REGEXEXTRACT(C1,"(.),(.),(.)"),A1:A3,B1:B3)),0)))
Without a separator
The value ABC
to be converted is in C1.
In this case we can't use split as it requires a seperator
=ArrayFormula(SUM(IFERROR(VALUE(SUBSTITUTE(REGEXEXTRACT(C1,"(.)(.)(.)"),A1:A3,B1:B3)),0)))