This video shows building the SMD HM board, so it really has very little in common with a standard through hole HM build. The through hole parts are much easier to solder than the tiny SMD parts.
I would suggest you watch some general soldering tutorials on youtube first, and then follow the build guide Bryan posted. It pretty much goes step by step, a few similar components at a time. One comment I have heard about Bryan's build guide though, the resistor color codes may be difficult to match to the resistors you have... so match your resistor values to the values marked on the board. (I'm wondering if Bryan identifies the resistor values for you in the kit? If not then measuring the resistance with a multimeter is probably the easiest way to identify them)
I generally place few resistors in the board then solder them and clip the leads, then do a few more... then do the capacitors the same. The resistors and the little yellow match head like capacitors have no polarity so it doesn't matter which way you insert them in the board, the larger can capacitors are polarized and have the - (negative) side marked on them. The diodes have a bar on them to mark their polarity and the transistors have a flat side, these details are all outlined on the board so orient those parts the way you see them on the board. All the smaller transistors are the same, except there is one MCP-1700-33 voltage regulator that looks the same as the transistors, so make sure to get that in the right place.
It's really not all that hard to do, the LCD mounting is probably the most challenging part...