Some of the other responses link to good resources, but I want to point out that "separating the code from the markup" is the wrong question -- instead what you want to do is separate business/application logic from display logic. It's okay to have an "if" statement or a "for" loop in your markup (in fact, it's necessary for dynamically outputting content), just make sure those things are specific to the display of the data, and not the creation or retrieval or "processing" of the data. For example, gat all of your data from the database first, put it all into a simple array or simple variables, then just loop through arrays and echo variables in the markup. MVC frameworks will have you put the data retrieval and prep steps in another file altogether, but even if you don't do this, at least shove all of that stuff up at the top of the php file and then at the bottom do all of the markup/display stuff.

UPDATE: Here's a stackoverflow link with a zillion more examples and resources about this: http://stackoverflow.com/questions/62617