You have to run Half-Life once before you can install. There's some directories that ESF needs that aren't created until you give HL a whirl atleast once. Just load up the training mission and exit.
On a side note, read the stickies and/or use the search feature. This question gets asked all the time 'round here. o_o
I have all the right requirements to play ESF, but the install button is greyed out!
You need to have run Half-Life at least once before you try to install ESF. To do this simply start a single player mission. You may exit the game once it has loaded up. After you have done this, you should install ESF.