#wrapper {
    width: 500px;
    border: 1px solid black;
    overflow: hidden; /* will contain if #first is longer than #second */
}
#first {
    width: 300px;
    float:left; /* add this */
    border: 1px solid red;
}
#second {
    border: 1px solid green;
    overflow: hidden; /* if you don't want #second to wrap below #first */
}