Are their steps to enhance Linux security?

To start off I haven't been using Ubuntu for very long, about a couple months, and I am not asking how to run or install something. Basically, I have been doing research for my networking class about security with Windows and Linux OS's and I read that for best security it is to not using the admin account. So would it be more secure by locking the admin account and creating a new one with fixed privileges? Are there any other tips or tricks for making my computer a bit more secure? I know it is a bit harder to get something malicious installed on a Linux machine but I want to know what kinda of things to be careful with. I apologize for any misspellings or grammar errors, I don't really feel a need to correct myself right now. =P