If you do a google search for “increase file upload limit wordpress” or some combination of similar words, you see the same advice repeated all over: change your php.ini file so it reads something like
upload_max_filesize = 10M post_max_size = 10M
(possibly including an execution time variable as well), and/or change your .htaccess to read:
php_value upload_max_filesize 10M php_value post_max_size 10M
Which literally does the same thing at a different level. If you’ve done this, however, and your “add new media” screen STILL says a ridiculously tiny number, and you happen to be running a multi-site install, there’s one more place you have to edit: under the network admin, under settings > network settings, there’s a maximum file size textbox. It’s in KB, so you’ll have to add some extra zeros, but that should take care of the problem.
WordPress is weird that way.