I used the following programs:

Linux Mint 15:
-Nemo

Android:
-VLC (https://play.google.com/store/apps/details?id=org.videolan.vlc.betav7neon)
-File Manager HD (https://play.google.com/store/apps/details?id=com.rhmsoft.fm.hd)
  -OR File Manager (https://play.google.com/store/apps/details?id=com.rhmsoft.fm) for phones

1. Just get a folder on Linux, right-click.

2. Press 'Sharing Options', share the folder and allow guest access.

3. Go to File Manager HD. Press the Network button. Scan. Wait patiently. (I assume  your LAN is on and both devices are connected.)

4. You will see an IP address. That's probably your computer. Press it. Navigate to your shared folder.

5. Play videos and enjoy. (Or not...)

Some videos don't work. Shared folders from partitions don't work. And it's slow sometimes. That's just how its security measures work (I assume). Fortunately, there is a workaround.

6. Go to /etc/samba/smb.conf on your Linux. Use root access and make a backup of the file.

7. On Gedit, Ctrl-F to find 'Workgroup'

8. Underneath the 'Workbook' line, add:

force user = UsernameThatYouUsedToShareTheFolderWith

Needless to say, put your username after 'force user'.

9. Then Terminal:

sudo service smbd restart

10. Repeat steps 3-5 with greater success. Some files may take longer to load than others, but the setup should be fine. VLC loads a lot of file formats though the native video player can stream most formats. You'll notice browsing in the shared folder is easier now.

Previous files that refused to work should work now. Shared folders in partitions can be accessed now.

This setup MAY reduce your security, If you feel your network must be as secure as possible, then you may not want to try this.

Visit this for more information on my original attempt to set this up and the troubleshooting afterwards: http://forums.linuxmint.com/viewtopic.php?f=90&t=150251&p=784767