I'm a new Dm and can't find answer anywhere else, is it a good way to implement fighting styles during a campaign? Should it be done between sessions, or should we just do it on the fly as the characters level up? Would it become a bit boring for the other players while fixing fighting style, or is it a quick enough prosess?

Do you mean fighters and other martial classes changing their fighting style options? 

I'd personally allow them to change it at level up but not on the fly every session. 

Yes, i ment fighters and martial art ussers. Thanks for awnser

To go into a little more depth. 

If someone picked a fighting style but didn't like and wanted to swap to another permanently, I'd let them do that once to help them enjoy their character more. 

I think swapping it every long rest through would be a bit much especially if they're just doing it to try and always have a better style for a certain situation or if they're say wanting to switch because the party just found a really cool magic weapon and they need another style to get the most out of it. For stuff like that I'd keep it limited to level ups.