You can disable any program by pressing Ctrl+Alt+Delete and entering the Task Manager. From there you can highlight the relevant program and click on 'end task', 'end process' or 'close application'. (The actual wording might vary between different version of Windows).
Restarting your computer will relaunch Zone Alarm (which I assume is the programme you're referring to). Note that installing Zone Alarm automatically switches off the built-in Windows firewall but disabling Zone alarm won't automatically switch the Windows firewall back on again. If you disable Zone Alarm you'll be left with no active firewall (which might be necessary to install anew piece of software but is generally to be avoided).
If you want to stop a program automatically starting when you turn on your computer, go to Start > Run, type 'msconfig' and click 'OK'. Go to the 'Startup' tab and click to remove the tick alongside the relevant program. Click 'Apply' and 'OK'. Restart your computer and, when you see a box telling you that you're using 'Selective Startup', click to put a tick alongside 'Don't show me this again'. (If you want to switch the automatic start-up function back on, simply go into msconfig to replace the missing tick).
Chris