First you need to go to mikescnr.com/adminlogs
You will be asked to enter a username and password, see http://mikescnr.com/forum/index.php/topic,201.0.html for information on that.
Once inside you will be greeted with a series of folders.
https://imgur.com/NdYD44I
There are different logs for different things, but I personally only really use FullServerLog as it contains all the AC messages, death messages, commands, and chat. The other ones only contain certain types of messages or errors.
Clicking on the FullServerLogs folder reveals a crapload of text files, one dated for every day since the server started running.
Opening one of these reveals a lot of useful information, you want to look for the ones at the bottom generally as they are the newest logs.
A few examples of what some of the common messages look like
death message
[0:07:05] Player NIGHTBIRD died. Killer: Stalenin Reason: 28 (Micro Uzi (Mac 10))
command
[0:06:16] Player Samone_dastroXD entered command: '/beta are u an old player?'.
chat message
[0:05:38] Samone_dastroXD: till i find crims
You can use the search feature of your web browser to find information you are looking for.
https://imgur.com/QFvqGUM