By default, mIRC saves its settings in an "mIRC" folder in the Windows Users folder.
In Windows 7/8, the path to the folder will look something like C:\Users\YourName\AppData\Roaming\mIRC
In Windows XP, the path to the folder will look something like C:\Documents and Settings\YourName\Application Data\mIRC
To copy your mIRC settings to another computer, you will need to copy this "mIRC" folder to the same location (based on the Windows version, as above) on your new computer. You can then install mIRC on your new computer as usual and mIRC should use these settings automatically.
Another way to find this folder is to run mIRC, open the "Tools" menu, and click on the "Received Files" menu item. This will open Windows Explorer at the "download" folder in your mIRC folder. You can then backup the whole "mIRC" folder and copy it to your new computer.