How can I tell if my mac is charging?
The light on the MagSafe adapter will be orange. You can also check in the menu bar if you enable "Show battery status in menu bar" in system preferences > energy saver
Also, do I have to turn off the computer to charge my battery?
No
What is the best way to get the most out of my battery, keep it plugged in? use with out the electric being plugged in?
If it is convenient then keep it plugged in, but for extended time like weeks, let it run down about 15% every few days.
Also don't let it run out completely, again only if it is convenient.
To be honest just use it when and where you need it. Not doing the above is not going to do massive damage to your MacBook, they are just tips which you should bear in mind and follow them if doing so is not detrimental to your work.