Can't upload plugins through WordPress, or insert images either. What am I missing?

Did you follow an article on installing Wordpress? If so, can you please link it?

Also, where are your files stored?

I installed WordPress on Ubuntu 12.10 through the applications tab when creating my droplet. The files for the install are stored in: /home/wordpress/public_html

Can navigate to your public_html directory and execute:

ls -l

What's the owner:group of the various files?

Run the following command:

usermod -a -G www-data wordpress

Does that fix it?

Here's what I did to get updates working, fix permalinks, and allow plugins & themes to be installed from the dashboard. These came from the user comments in this post: https://www.digitalocean.com/community/articles/one-click-install-wordpress-on-ubuntu-12-10-with-digitalocean

To fix auto-updates:
chown -R www-data:www-data /home/wordpress

To fix permalinks:
1) Enable Mod Rewrite : sudo a2enmod rewrite
2) Change AllowOverride None to AllowOverride All : sudo nano /etc/apache2/sites-enabled/000-default
3) Restart Apache : service apache2 restart

romerornd just saved me a lot more annoyance than I was already. chown -R www-data:www-data /home/wordpress was enough to get me going again. Thanks again!

Thank you so much guys. The following commands has now allowed me to update my wordpress!

chown -R www-data:www-data /home/wordpress

Thanks again!

thanks guys it works for me but i want to know that what "chown -R www-data:www-data /home/wordpress" exactly does ? is there any requirements of undo this or is it secure.? plz guide me.

thanks.

@Nishant: It changes the ownership of all the files and directories in /home/wordpress to the www-data user so that wordpress can overwrite its files when updating.