Check the install section of the plugin, I has all the steps you need to complete to make it work.
http://yoursite/wp-admin/admin.php?page=w3tc_install

PECL Alternative PHP Cache (APC) Installation (Recommended):
Time required: 1 minute

Install APC using the PECL command (and skip to #5 if successful):

pecl install apc

Or via compilation. Download the latest stable version and extract:

cd /usr/local/src && wget http://pecl.php.net/get/APC-3.1.9.tgz && tar -xzf APC-3.1.9.tgz && cd APC-3.1.9

Note the paths returned for the following commands:

whereis php-config whereis apxs

Use the output from #2 to modify the --with-apxs and --with-php-config flags in the following compile command:

phpize && ./configure --enable-apc --enable-apc-mmap --with-apxs=/usr/sbin/apxs --with-php-config=/usr/bin/php-config && make && make install

The result should be similar to:
Installing shared extensions: /usr/lib/php/modules/
You can also use the apc.ini file we prepared for you:

cp /var/www/vhosts/domain.com/httpdocs/wp-content/plugins/w3-total-cache/ini/apc.ini /etc/php.d/

Restart apache when ready:

/etc/init.d/httpd restart

You're done! APC should now be available. If the following command retuns anything, you're all set:

php -r 'phpinfo();' | grep 'apc'