As the title suggest, how will I know if I’m on Joomla! home page?
for example:
if('ImOnHomePage'){ do this... }else{ do this instead... }
A quick answer should be via PHP $_SERVER global variable:
<?php $uri = $_SERVER['REQUEST_URI']; if ($uri == "/" || $uri == '/home.html') { echo 'Im on home page'; }else{ echo 'Im not on home page'; } ?>
Please before trying to update or change your templates/TemplateName/index.php file please do make a backup. It can save your life 
fatal error: Allowed memory size of 8388608 bytes exhausted?
Ran into this? chances are your memory limit is set to only 8MB, which is rather low for most of the scripts. Lucky you I discovered a quick fix and save you from the frustration trying to fix this
Ok, let me share what I found.
Open your configuration.php file located at the Joomla root folder, and insert this tiny little script just after the PHP open tag.
For example
<?php ini_set('memory_limit','12M'); //recommended is 32MB, so they say but ill will put 12M for this example //rest of the script follows...
save your configuration.php file and reload your page. Works like a wonder , Yes?
UPDATE: BTW for some reason when you installed Joomla and admin page is somewhat lost and scattered, This little code can fix it. I think you know the reason…ok chow