If you are using Apache, I would start here.
Compression and caching are different things.
For compression, PHP Minify or YUI Compressor are great. If all else fails, TextMate has a nice Javascript Tools Bundle that allows your to compress your code. You could manually compress your code, then upload it, and undo the compression to get the source back to a readable state. I do not recommend this, but I have done it before.
For caching, read the askapache.com site. There are several easy ways to turn on mod_expires, mod_compress, and other modules. Since you are on shared hosting, here are caveats because the host may have turned off certain Apache modules. I have used GoDaddy, and they turn off mod_expires. For host specific information about Apache modules refer to the hosts support documentation.
If you are luck, the important ones are on and you can:
<IfModule mod_deflate.c>
SetOutputFilter DEFLATE
SetEnvIfNoCase Request_URI
.(?:gif|jpe?g|png)$ no-gzip dont-vary
</IfModule>
<IfModule mod_expires.c>
ExpiresActive on
ExpiresByType image/jpg "access 2 month"
ExpiresByType image/gif "access 2 month"
ExpiresByType image/jpeg "access 2 month"
ExpiresByType image/png "access 2 month"
ExpiresByType text/css "access 2 month"
ExpiresByType application/x-javascript "access plus 2 month"
ExpiresByType text/javascript "access plus 2 month"
ExpiresByType application/javascript "access plus 2 month"
ExpiresByType image/x-icon "access plus 12 month"
ExpiresByType image/icon "access plus 12 month"
ExpiresByType application/x-ico "access plus 12 month"
ExpiresByType application/ico "access plus 12 month"
</IfModule>`
Put this code in your .htaccess file, open FireFox, then Firebug, then YSlow. Run the YSlow test, it will let you know whether the caching is working.
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