I havw always wanted to try WoW and since I can play for free up to level 20 I figured I would try it out. My problem is I am level 3 and I just learned a new spell, but I have no clue how the hell to put it into my hotbar with the other 2. Since I am a noob a good explanation is needed thanks.

I opened up the spell tab and cannot click and drag it to the hotbar and it does not add it to the bar automatically. It is the downloaded version if that makes any sense

Hitting P (default key) and click-hold and drag the spell onto your bar. That's how it's done. If you can't do it then there might be a problem. Open a ticket with a GM if you really can't do this.