For those who do not know what a keylogger is, it is a program that keeps track of what has been typed on your computer. There are two different types of keyloggers: rogue and non-rogue.
Both of them do the exact same thing: keep track of what has been typed on your keyboard. Rogue keyloggers are installed on your computer without your knowledge and they send data to some third party. The non-rogue keylogger is installed on the computer with the user knowing about it being installed and what ever data it gets is sent to the computers owner.
You can not really tell if the computer you are using has a keylogger installed, but the best way to determine if your computer has a rogue keylogger installed is to run a malware scan on your computer. Malwarebytes (free for non-commercial use) does a pretty good job at detecting threats from malware. Some other things you can do to stonewall keyloggers include using a p*word manager that has the feature to auto fill p*words. A few p*word managers you can trust include RoboForm, KeeP*, and P*word Safe. An other option you can use is an intrusion prevention system.