How and when you do apply for in-state tuition at university?

Your residency status is assessed as part of the normal admissions process, based on information supplied in your application.
If you need to establish residency, you need to petition the school for a change in your residency status. You would need to contact the university directly to get access to the correct forms to fill out. You should do this at the same time as submitting your application to the school, although if your status changes you can do it at a later date.

You don't "apply for in-state tuition". You apply to the school, period. If you have already established state residency, you will automatically be admitted as "in-state".
If you are admitted as "out-of-state", you cannot change your status at any time during your bachelors degree. You will be considered "out-of-state" for your entire undergraduate degree. This is because, to establish residency, you must do so BEFORE you begin attending school; the time you are attending school does not count.