The command to find files older than 30 day is this:
find /path -type f -name \*.log -mtime +30
How you go on from that depends on what you mean by "archive". If you use software like IBM TSM, you'd write the result of a file and use that for the dsmc command. If you just want to move files one-by-one to a given location, you can add a -exec action to the find command.