Parent Div Content Overrunning Child Div Content

Hello all!

I have been doing web design now for about a year and this is the first time I have had a question that I have not found already answered in a forum or book somewhere, so it would really make my day if you all could help me out

I'm trying to have a parent div, with content, and a child div below it with content and not have the two running on top of each other. Here is visual of my goal:

***************************
* |Parent Div| *
* *
* content content content *
* content content content *
* content content content *
* ********************* *
* * |Child Div| * *
* * * *
* * different content * *
* * different content * *
* ********************* *
***************************

I can get the child div at the bottom using CSS:

#childdiv
{
    bottom:0;
}

The problem is no matter what I try, the parent div's content runs into the child's!

So I have this:

***************************
* |Parent Div| *
* *
* content content content *
* content content content *
* content content content *
* ********************* *
* *con|ehtlcoDtventcon* *
* *dciofnftentatnlwrwe* *
* *dciofnftentatnlwrwe* *
* *dciofnftentatnlwrwe* *
* ********************* *
***************************

Additional info: I can't use fixed height, or else I know a workaround that would have helped >.<

Here is the html:

<div id="parentdiv">
<div id="childdiv"">
<p>Archives</p>
<a href="oldblog.html">Old Blog</a>
<a href="oldblog.html">Old Blog</a>
</div>
<p> My content</p>
</div>

I have tried "clear: both;", setting margins, padding, and now I really don't know what else to try. Any help would be greatly apprecaited!
PS

I didn't post all the code because most of it is not essential.

Thanks again for any help!