overflow , one div
#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 */
}