Yes it is very important that you get away from using your arms and try to use your wrists/fingers primarily, your arms should be used for big accents only. This should come naturally with time but you do need to pay attention to this, then as you move onwards you should start to use the natural bounce of the stick to get extra hits out of your strokes, both these concepts are fundamental to drumming.
You don't necessarily need formal lessons for this and the rest of your technique though, there are plenty of videos out there that explain things just fine. Mark wessel's (on vicfirth) and Dom famularo's (on youtube) various videos are great for this. I did fine with this method anywho, I have a teacher now and he say's my technique is great, you just have to pay close attention to what your doing, start real slow and spend alot of time getting your weaker limbs up to speed.
The key is to stay relaxed and loose at all times, if you tighten up or feel any pain then your either going to fast or adopting the wrong technique.
Some important techniques to look up when you've been drumming for a few months are 'the free stroke', 'the moeller technique' and 'open/close (also known as push/pull)', learning these will really help you out.