Enroll in a community college for a Ukrainian language course or in a local language teaching center. You can also look at online courses available for learning Ukrainian.
Study the grammar and language linkages of Ukrainian by going through the relevant study material that is easily available online.
Practice writing the Ukrainian language on a regular basis and study the language textbooks in detail.
Read the literature written in Ukrainian language extensively. Start from newspapers and short stories and move to advanced texts as you gain some mastery over the language.
Befriend a person who is a native Ukrainian speaker. Communicate with your friend exclusively in Ukrainian as it will help hone your speaking skills.
Listen to audio tapes and watch videos in Ukrainian on the Internet to give you an idea of the breadth and depth of the language.
Keep the Ukrainian dictionary very handy. Whenever you come across an unfamiliar or new word, look it up in the dictionary and try using it in your vocabulary frequently to cement it in your brain.
Practice reading and writing the Ukrainian language with a personal tutor. You will have to spend a little money on this but it will go a long way in making you learn the language.