I am a ballroom dancer, have been for 8 years, so I can offer you some tips.
Generally, if you are planning to slow dance with your date, the steps are very simple. All you need to do to a slow song is shift your weight from foot-to-foot at a speed that works with the music. Just put your feet apart about shoulder width or a little less, and just rock gently back and forth left to right. You can slide your feet in any direction as you do this, and generally your partner will feel it and follow suit. To avoid feeling akward, keep your knees just slightly bent, and let your hips/body move with your weight changes. This absorbs the movement from your legs and prevents you from looking stiff or choppy.
I am describing a dance called the Foxxy. It is what everyone tends to do when they are slow dancing because it is really easy to do. You will look really smooth and cool if you do it, and be the envy of other dancers.
As far as arms are concerned, you two can put your arms however they are comfortable. A lot of young couples choose to put the guy's arms around their waist, and the girl's arms around his neck. You can also have him put his right hand on your back, rest your left arm on top of his and put your hand on his back or arm, and he can just hold your right hand in his left hand up high or down low by his waist, whatever you prefer.
If you want to fast dance, just move your feet rhythmically and move your body to the beat however it feels good.
Most importantly, just have fun and be sure he knows it. You always feel better when you start dancing and see how easy it is. You will do great!
