If I Don't Wire USBASP to ATmega 328-PU Will I Burn Out My Chip
Yes, that is quite possible, so do not miswire it.

What you could do is try to defend the chip from yourself. For example, you could put some resistors, say 220 ohm, on the MISO, MOSI and CLK lines. This will give you some safety from bad connections. 

Of course, this won't help you if you connect GND to Vcc, since you can't have resistors on those two lines. 

If you have any doubt, use a multimeter. If you get to the point where you're not sure what you're doing, make a break and try it in 20 minutes or next day or whenever you're a bit more rested.