Typically on a linux VPS that does not have Plesk most logs for services like http, ftp, and mail (depending on what kind of mail and FTP programs you install) can be found here:
If you have Plesk then in addition to the above you should also look in the following directory (specifically for maillogs):
If any logs are showing as constantly empty then you might not have the syslog service running or installed.
To install it on a CentOS VPS first install yum (if you haven;t done so already):https://support.blacknight.ie/index.php?_m=knowledgebase&_a=viewarticle&kbarticleid=209
And then run the following command:
# yum install sysklogd
If you have a Debian VPS then you use apt-get instead of yum. First you need to find the package name for the syslog service:
# apt-cache search syslog
Then install it using:
# apt-get install PACKAGENAME
where PACKAGENAME is the package name you get from the first command.