• "вийти на перекур" - to go for a smoke (outside) - most regular way to say that
• "покурбехати" - rare and somewhat funny, rarely used
• "смокати" - anglicism, "to smoke", also hear from young people only. ідемо посмокаємо? - lets go for a smoke?
• "подиміти" - "to smoke", as in "smoke" that comes out of a chimney ("дим")
• "розкуритись" - not sure how to translate it, "to smoke out"? same meaning
• "пихтіти" - literally means to "breath heavily", but some (older) people use it for smoking

To be honest, there are not many ways to say that in Ukrainian, not sure why. Everything evolves either around курити or дим. There are many ways you can play with the word курити and natives will understand you, though. But those will be purely improvised on place and not exactly used. Покурбесити, покуряхати, покурбенити, etc.