1. Find the url to the latest version of fileinfo from
http://pecl.php.net/package/Fileinfo

2. Download, compile and install
wget http://pecl.php.net/get/Fileinfo-1.0.4.tgz
gunzip Fileinfo-1.0.4.tgz
tar -xvf Fileinfo-1.0.4.tar
cd fileinfo-1.0.4
./configure
make
make install

3. Add extension=fileinfo.so in your php.ini file

4. Restart Apache