If all you are trying to do is simply upload files, then there is no need for a database.
Here are some things to double check if File upload is not working:
1) To be able to upload a file, the forms encoding type must be set to multipart/form-data. Dreamweaver will do this for you automatically if you add the file field by going to Insert -> Form -> File Field. If you add the file field manually, you will need to change the encoding type.
2) Make sure the forms method is set to post, you cannot upload a file using the GET method.
Here is an example form:
<form action="" method="post" enctype="multipart/form-data" name="form1">
<input type="file" name="fileField" id="fileField">
<input type="submit" name="button" id="button" value="Submit">