Chances are you are clicking the icon. Are you new to mods? This information will help with all mods...
Do you have half-life or counterstrike? Just quickly make sure both are upgraded all the way.
Start up either of these games, and click custom games(it might be called Mod Listing in CS, not sure...) Then find ESF and activate it.
Another way to start the mod is to use this shortcut : C:\SIERRA\Half-Life\hl.exe -game esf -console
If you have counterstrike then the path will be different, but it will still have the "-game esf" part in front of it.