Leo - I originally started to try and work from a transliterated version and didn't really find it easy , as some of the vowel sounds were just not quite right.
Fr Archmandrite Serge told me I really should learn to read Ukrainian and I said I was too old.

I worked from a bilingual version - Cyrillic script and English and still do.
I now can read Ukrainian - but I'm slow , but I have read aloud in Church using Cyrillic Script , after suitable practice

.
Find a copy of all the letters in the Ukrainian alphabet and how they sound in English and are used in a word in Ukrainian- then slowly start to learn to read them - simple words at first and then progress.
Strangely enough one of the things that's helped me greatly is reading aloud the headlines from the BBC News Site in Ukrainian each day
BBC - Ukrainian [bbc.co.uk]