I'd say the times when you are most at risk of frying are while you are putting it all together. Just be sure to properly ground yourself by touching the inside of the case. Also, be sure your motherboard is attached to the case properly before hooking it up to power. If it is touching the case somewhere it shouldn't be, you are gonna fry it. If it doesn't seem to be fitting properly, chances are you are doing something wrong. The riser pins should line up perfectly. The motherboard output jacks should line up to the back of your case perfectly. The PCI cards etc., should line up perfectly with the back of the case etc. Many people fry their motherboards at this stage.
When handling parts, don't touch the circuitry.
And depending on your CPU and heatsink, it can be REAL tricky to get that heatsink on sometimes. Do not put too much pressure on the CPU when applying the heatsink. And don't wiggle the heatsink (don't rock it back and forth). It does take a fair amount of pressure to get that heatsink on, and with experience you get to know the balance of what is too much. Just be careful...
And yes, you should install the major components first before turning on the power. No need to install unecessary parts at first, just the basics. Vid card, HDD, ram and see if you can post (get into the bios).
Good luck!