If you want to modify files in /var/www/domain, you can simple change its ownership to your user:

sudo chown -R youruser:youruser /var/www

That will give your user write access to all of the directories/files in /var/www.

Check out How To Use Filezilla to Transfer and Manage Files Securely on your VPS.

Also, make sure that your /var/www directory is owned by www-data:www-data; by executing, in a terminal,

ls -la

If it's anything but, execute:

sudo chown -R www-data:www-data /var/www

Also, make sure that your user is part of the www-data:www-data group, by executing:

sudo usermod -a -G www-data username

Did you implement Step Four of Initial Server Setup with Ubuntu 12.04?

And even if you have implemented step four you still need to run the command with 'sudo' in order to gain root privileges.
ex.
#sudo mv directory /home/user/targetdirectory
#sudo shutdown -h now

sudo nano /etc/sudoers
add your username
done

Followed the steps to the letter, and already added user ALL=(ALL:ALL) ALL to the above, still causing me some issues.

So sudo mkdir ~/test does not work for you?

Have you tried rebooting your droplet?

Remember that with Linux, names are case sensitive.

Using terminal yes that's possible, but there's two factors there.

1. I'm in /home/user/
2. I'm using terminal rather than ftp app like transmit

The reason I want to use SFTP is because I do a lot of work with Expression Engine and need to be able to just upload files.

Could I just put my domain folders that are being pointed at in /home/user/domain etc, if so is that a complicated task changing where things point to. I'm fairly new to all of this.

Just to add to above, currently my sites are in /var/www/domain/