Dial "011." This is the international exit code for the U.S. and Canada. Dialing it tells the telephone system that your call will be routed to another country, and that the next set of digits will be the country code to perform that routing.
Dial "380," the country code for the Ukraine. This will route the call into the Ukraine's national telephone network.
Dial the local phone number, including the two-digit area code. If you don't know the area code, but do know the name of the region of Ukraine you are calling, you can look it up online. For example, the code for Kyiv, the capital city, is "44." To call the number "123-4567" in Kyiv, you would need to dial "44-123-4567" after entering the international exit code and the country code. Ukrainian mobile phones have a two-digit network code instead of an area code; you will need to add this in the same way.
Wait for a ring. If you don't hear anything after 30 seconds or so, hang up and try again. Telephone networks can get busy at peak calling times, and may not put your call through. If possible, call back at another time.