Parsing is usually implemented in two steps: first there's lexing where the input is turned into a sequence of tokens, then there's proper parsing where the sequence of tokens is turned into an abstract syntax tree. This shunting yard algorithm is part of parsing. Lexing happens before that.

For example, this input:

    13- 2  *5 + 4

would be lexed into this sequence of tokens:

    "13" "-" "2" "*" "5" "+" "4"

You could use the shunting yard algorithm to put these in a convenient postfix order:

    "13" "2" "5" "*" "-" "4" "+"

It's really easy to then turn it into an abstract syntax tree (AST). Go through each token in order: if it's a number you make it into a node and push it onto a stack; if it's a binary operator you pop two nodes off the stack and make a node out of those and the binary operator. If you write down this AST as an s-expression you get:

    (+ (- 13 (* 2 5)) 4)