you upgrade a quickstart package just like you would any other joomla install
you go to this page
Joomla Downloads
in your case you look for a patch for 1.5.3 to 1.5.6
there are two on the list, if your on a windows computer, download the .zip one to you local harddrive
put it in a folder all by itself and then unzip it.
go to your ftp program, i recommend filezilla.
the unzipped file will have the structure of a joomla install
DO NOT UPLOAD DIRECTORIES
you need to upload and replace each individual file individually
component files go to the compoinent directory, upload each individual file in each folder one to one.