Bring flowers - Flowers play a much more important role in Ukraine than they do in the West. A single rose is appropriate for a first date. If you meet your lady's family, be sure to bring flowers to her mother. Always buy an odd number of flowers (even numbers are used at funerals). Also, never buy yellow roses (can signal a decrease in feelings or the end of a relationship).
Dress your best - Ukrainian citizens do not share the altruistic "looks aren't important" mentality that has spread through the West. First impressions are very important to them. You will notice that on the street, people will look first at your clothes, then at your face.
Don't try to shake hands - Women in Ukraine do not consider it feminine to shake hands when they meet. Also, in the winter, make sure you take off your right glove before you shake hands with a man. To fail to do so is considered rude.
Offer your lady your arm - Usually, men and women do not hold hands in Ukraine when they walk together. Instead, the woman takes the man's arm. Be sure you always offer your arm to your lady when you cross the street. Help your lady onto/off of vehicles. Many Westerners are not accustomed to using public transportation systems and forget this courtesy. When the two of you get onto or off of buses, trams, taxis, etc., always extend your hand to help your lady.
Always do the pouring - When at dinner or at a bar, always make sure that your lady's glass is full. The man always does the pouring. This is an old custom but very deeply ingrained. If you forget to do this, she may think you have no table manners.
Don't drink much alcohol - One of the main reasons Ukrainian ladies are interested in Western men is that alcoholism runs as much as 50% among males in this part of the world, which causes them to be less than desirable husbands. Therefore, when it comes to drinking, you should always show moderation and self-control.
Take off your shoes in her home - To avoid bringing dirt into their homes, Ukrainian citizens almost never wear their shoes inside. Instead, they wear slippers. They usually have an extra pair or two for guests near the front door. If they don't, simply take off your shoes and remain in your stocking feet (Note: because of this custom, you might want to pay careful attention to the socks you choose to wear).
Attitudes about sex - You will find that Ukrainian women have the same (i.e., modern) attitudes about sex as Westerners do. Specifically, a few will engage in sex on the first date, a few will not engage in it until they are married, but the vast majority fall somewhere between these two extremes -- they will have sex when they feel that a certain level of mutual caring and trust has developed in the relationship.
Asking for her hand - It is still an accepted Ukrainian custom to ask the woman's parents for her hand in marriage. If geographic distance is a problem, consider a phone call. Your fiancée may not think this is important or even want you to ask her parents, but at least make the offer. Remember, if the woman still lives with her parents, you do not want to offend them by failing to respect an old Ukrainian custom.