Try to keep up with current affairs. Don't criticise her unless you cannot avoid doing so. She can be very highly-strung, and may react negatively. At the same time, if there is anything that you feel needs to be discussed, you would be better coming out with your comments directly, rather than being obtuse. She will expect you to be completely honest.
Many women find Geminian men difficult to understand.
They are often very charming and successful in life. At the same time, their very intellectual approach to relationships can make them seem a little cold. They are slow to warm up emotionally, and do not readily share their feelings. The way to a Geminian man's heart is through his intellect. However, don't try to interfere in his business or professional concerns unless it is clear that your advice is welcome.