The best way is just to take an overnight train "Kyiv - Kerch" #222K or #28K. The train ride is nice and comfortable, with a restaurant carriage. But it is quite long (approx 21 - 23 hours)

• By plain & bus (fly to Simferopol and then take a bus to Kerch) (Boryspil airport)
• By bus (There are no straight buses to Kerch, so it's possible to get there with changes in Simferopol, Sevastopol, Yalta or other cities)