Increasing the maximum upload file size to WordPress can be done in several ways and largely depends on your servers configuration. The way it works for me on my dedicated server running cPanel is to upload a php.ini file into your /wp-admin folder with the following values

upload_max_filesize = 32M
post_max_size = 32M
max_execution_time = 300

Feel free to download this file with the above configurations already inserted. (Please extract the php.ini file out of the .zip file and then upload it into your wp-admin folder)