I am attempting to write a shell script, to become part of a cron, that will check the date/time stamp of files in a specific directory for file older the 24 hours. Then create a tar file of the identified file and remove the old files. I currently have the process to locate the old files using 'find':

find /<path/to/directory/> -mtime +1 -type f -exec ls -la {} \;

But am lost. Any help would be appreciated.

Well, you're 99% of the way there.

Using your find command, which is giving you a list (forget about the -exec ls -la {} \; part, you don't need it for what you want to do), simply use find to get a list of files in a temporary file (say, /tmp/filelist or something). That would be
Then, create your tar archive
Then, use the same list to remove the files
Just in case the list of file is quite large, you can use find to do that instead (and here's where you can use -exec)
or you could use xargs
Finally, remove the temporary file
Wrap that up pretty in a shell program and viola!

Hope this helps some.

Thanks for the pointers. This was very helpful. I did have to go with find <path-to-direcoty> -mtime +1 > /tmp/filelist -exec rm {} \; due to the immense file size. I have been able to successfully create a cron with this and a few other commands that does what I needed.

Something I forgot to mention above (twice, now) was that it may be useful to restrict find to looking only for files (or not to look at directories as it were); e.g.,
If there are any sub-directories involved they will show up in the list using -type f so there's no problem doing so.

Anyway, glad to know you got going.