Mount PCB in a vise, so that it won’t move while you work on it. The board was designed mostly for 0603 component size, but you can fit 0805 components without much trouble.
Before you begin, here’s a quick SMD soldering tutorial you might find useful:
Place solder on one pad of the atmega328p footprint. Align the 328 chip to pads and solder that pin and pad. Check the overall alignment of the chip to the pads and adjust now if needed. Then solder one more pin on the opposite sides, this will lock the IC in place while you solder the other pins.
The dot on the chip has to match the dot on the board (upper left corner of the PCB pad).
To make soldering easier and solder reflow better add flux on all pads/pins. This will also help prevent solder bridging. The easiest way to apply flux is with a bottle with a syringe needle attached, or even more convenient – with a flux pen.
Solder all the MCU pins. Less soldering results in less problems, less in this case is better. Double check your work, make sure you don’t have any solder bridges! Do you see any? With SMD work, a stereo microscope is a great tool to have both to see what you’re doing, and to inspect small components. Can you spot a bridge in the photo below?
Another indispensable tool for SMD work and rework is a hot air station, they are quite affordable these days. If you do lots of SMD work, make your life easier and add one to your tool inventory!
Use hot air to solder the 1uF and 100nF caps, 10k resistor are next. Here the capacitors size is 0805. If you don’t have a hot air station, use tweezers to align-hold the part in place, and tin the side where you had solder on the PCB pad. Then add flux if needed, and solder the other side. Move on to the LED and its resistor.
After all components are soldered, use isopropyl alcohol and Q-tips to dissolve and clean flux and other soldering residues. Hopefully everything looks nice and shiny!