How do I manually mount a linux file system read/write as a normal user?

On an ext4 filesystem (like ext2, ext3, and most other unix-originating filesystems), the effective file permissions don't depend on who mounted the filesystem or on mount options, only on the metadata stored within the filesystem.

With Ubuntu, mounting should happen automatically when you insert the disk, or you should be able to click on an icon to mount. You can also install pmount to mount filesystems as an ordinary user from the command line.

If you have a removable filesystem that uses different user IDs from your system, you can use bindfs (in the Ubuntu package of the same name) to provide a view of any filesystem with different ownership or permissions. The removable filesystem must be mounted already, e.g. on /media/disk9; then, if you want to appear as the owner of all files, you can run

mkdir ~/disk9
sudo bindfs -u $(id -u) -g $(id -g) /media/disk9 ~/disk9

You can use:

mount -o user /dev/devicename and user option in your fstab.