This is not a very old alienware model. So I'm guessing you haven't had it a long time yet.
You're in luck if that's the case because it's probably not going to need to be opened up to be cleaned properly (though you may want to prepare yourself for that possibility in the future.)
simply put:
unplug it, and remove the battery this is because the compressed air will often generate a little condensation or even leave the can in a still somewhat liquid state so we want the power completely off even though the odds of it causing a problem are remote, better safe than sorry.
after that is done do an initial blow into the intake (usually underneath) then reverse through the output vent (usually in back) I would generally do this several times each way, as if there is dust stuck to the fan it has a habit of getting stuck on there on the leading edge of the fan and a little back and forth is your best bet of loosing it without opening the laptop.
To do a full and proper job of cleaning a laptop's insides you are really going to have to open it up though.
There's several videos on youtube that will walk you through the steps of doing so, though given the fact your confidence seems a bit shaky on the subject I'm not sure that is a task for you.
You can also take this opportunity to mix water and rubbing alcohol at a roughly 50/50 ratio, you can then put a tiny amount on a (preferably lint free) cloth and use it to clean the screen. Make sure the cloth is not dripping before using it. Regardless of cleaner you choose for that task you put it on the cloth, not directly on the screen.
they sell special cleaners for this task but almost all of them have the same two basic ingredients which are the aforementioned rubbing alcohol and water.
Many people make the mistake of using a household glass cleaner for this task, since many of them contain ammonia which can literally eat through the screen, I DO NOT suggest using a household cleaner on the screen of your laptop.
Give it a few minutes to be sure the compressed gas and (if you cleaned it) the screen are properly aired out and dry before attempting to power it back up.
as for using the straw. Yes I would suggest it for this application.
Just read the instructions on the can regarding the angle they want you to hold it at and whatever details may be located there.
p.s. they are very rarely compressed air but compressed gas. I would not suggest breathing any in directly.
