Learning Ukrainian on your own can be tough. Compared to French, Spanish or German it's not commonly spoken, so the online pickings are slim. These links have helped me:
BBC Languages Across Europe - Ukrainian - Web page from the British Broadcasting Corporation has some basic facts about the Ukrainian language. Also includes a few basic words and phrases which you can hear if you have a Flash Player plug-in.
Ukrainian Alphabet - This is a web page by Sergiy Synylo. The characters of the Ukrainian alphabet are shown with their English equivalents. If you have Real Player, you can click on the little speaker icons to hear the sounds the letters make.
Ukrainian As a Foreign Language - When this site is up, it has 11 free online lessons including sound clips by native speakers. According to the site, 'Ukrainian As a Foreign Language is a free online course for beginners. It offers eleven lessons containing basic vocabulary and grammar. You do not need to know any Ukrainian to take this course successfully.' Pretty good.
English-Ukrainian Vocabulary Quizzes- Self checking, online quizzes. Currently has 5 categories: colors, kitchen, economics, animals, and days of the week. Relies on volunteer /user input. Know a foreign language? You can contribute data for quiz.
Ukrainian Dictionary Online - Type an English word in the blank field, click the 'English-to-Ukrainian' button, the screen will refresh and the results will be displayed. Nifty.
Ternopilska Oblast Library for Children: Dictionary - This is a link to 'Useful words and phrases.' The site is written in Ukrainian, but it can be helpful to English speakers if you know how to sound out Ukrainian words. Click on the other BLUE bubbles for more words, ie. bubble on the far right for months, seasons, days; second from right for numbers. Also, check out the little cartoons in the top, left corner of each page.