I'm going to make some assumptions about your question, so if they're wrong, please edit your question to clarify. First, I am assuming that you have two Ubuntu systems, one that is a web server called
server that has your log files, and one that is a desktop system where you wish to download these files. Second, I'll assume that the server has
sshd running to facilitate remote access, and that you can log in as a user called
user with access to the log files.
To do this, I would run an
scp command on the desktop system:
scp -r user@server:/path/to/get/log/files /path/to/put/log/files