I have helped folks do stuff like this here before, and of course have wired up many setups myself.
It really is that simple, BUT......
The devil is in the details. If you had just a little more knowledge, I'd say go ahead and we can give tips.
But, the fact you had to ask means that you need a little more basics to tackle it yourself.
Just a few of the things you need to know, are: Size of wire. Size of breaker. Those we could help you figure from the name plate on the compressor.
But, does your panel have enough capacity to handle the extra load? That I cannot help with from here.
Also, do you have a place for another breaker? Just because you have some unused slots in the panel cover, does not mean that there are tabs under them for a breaker.
A lot of panels will not have a full set of connections on the power buss even though there is a full set of knockouts.
I have been bitten by that one before. I even bought one of those panels by mistake.
Got ready to install it, pulled the cover off and 6 of the breaker locations were blank.
I took it back to the store and got a full panel.
Considering the fact that if you wire it wrong, you could electrocute yourself or someone else, and even if you wire it right, you could burn the place down, I suggest you either get an electrician, best case, or at least someone with more knowledge then you have now.
If you absolutely have to do it yourself, at least post pictures and ask more questions before you try it.
Electrician is better, but I would rather try to steer you away from trouble than let you go it alone.
Remember, unless the other shop is exactly like yours, you can wire it exactly like his and still have big trouble.
First, because his panel may be rated higher than yours, or his service might be higher.
But, just because his is working, does not mean its wired right........ He might just be luckier than you.......
