Well first off, you'd want to tokenize the string. Essentially, separate each element. Separate the operations from the individual numbers, and store them in something (maybe a list). Then just go through the operations based upon the order of operations.
So the pseudocode would be something like:
public int eval(String infix)
{
create a list of all the elements
identify which operations you would want to do first
perform the operations and simplify the list (e.g. if 5x4 were inside parantheses, remove the parantheses and replace it overall with 20.)
continue the simplification until you have a final result
return the result
}
There are probably much better ways to do this, but here's one solution.