The microcontroller is to be mounted on the top side of the PCB.
Flash the microcontroller before you touch it with a soldering iron. For more information about verifying the working of your microcontroller, read How Do I Test My Microcontroller? This way you can make sure that it works, and can return it for a working one in the event that you received a broken microcontroller.
Align the microcontroller with the outlined columns of pads: it will be different depending on which half you solder it to. The microcontroller always faces with its backside up: the USB port will face down, closest to the Lily58 PCB.
Insert the header pins on the top of the PCB in the areas marked with a white outline. You can hold the headers in place by placing the microcontroller over the headers, and then applying some tape across the headers onto the PCB.
After holding it down, solder the headers onto the PCB.
Then, solder the microcontroller to the headers on the top side of the PCB, and trim off the excess header pin lengths.
When trimming the legs, take care to wear eye protection. I prefer to wear a protective working glove, and place my hand close above the cutting area to prevent tiny sharp bits of metal from flying around. The glove will keep my hand from being hit by the pieces. They can be quite sharp!
You can socket your microcontroller. To do so, first solder the sockets into place on the top side of the PCB, where you installed the TRRS jack and reset button earlier. The sockets should go in the row of holes with a white outline around them. Attach them to the PCB using a piece of tape, and solder them from the bottom.
I prefer to apply a piece of kapton, electrical or simply scotch tape between the sockets and the microcontroller to prevent solder from flowing down into the socket. This will make later removal easier.
Then, using diode legs you clipped off earlier, we can start on the second part. Place the microcontroller on top of the two sockets, and insert a leg into each of the sockets through the holes of the microcontroller board. After inserting the legs, solder them to the microcontroller, and clip off the excess leg lengths.
You should use pliers to insert the diode legs into the sockets. The sockets will provide a bit of resistance when pushing the legs in, which makes it hard and possibly painful to do by hand. You'll feel the legs "clip" into place when pushing them in.