Algorithm for AST [duplicate]

I'm creating a programming language in C ++. I made a simple lexer, which works perfectly fine for now.

out 5 + 7 * 3

My lexer turns this into:

kw:  out
num: 5
op:  +
num: 7
op:  *
num: 3
nl

Now I need to create an AST (abstract syntax tree), which makes the example into this:

   kw out
      |
    op +
    /  \
num 5  op *
       /  \
   num 7  num 2

But how do you do a tree algorithm?

Note Please do not post a code, that takes away all grace. Instead, tell me the logic of the algorithm.