The kit is meant to be soldered by the purchaser. The board already has the copper traces in/on it that connect the components; you just have to solder the parts to the little exposed pads where the terminals stick out. Check the instructions that shipped with the kit - it should tell you all you need to know about which part goes where and the best sequence in which to do the soldering. Typically the lowest profile parts are done first, like resistors and diodes (be sure of the orientation of the diodes), ending with the taller parts like the relays.
You'll need a soldering iron, a 30 to 40 watt iron with a fine tip will work well for this project, and good quality 60/40 rosin-core solder. Use a small diameter solder; it'll melt easier and you'll have better control over the amount. If you haven't done any soldering before, practice using the iron on some pieces of stripped wire or scrap PCB if you can get hold of some. Don't overheat the parts when soldering - just leave the iron on the terminal long enough to get a clean, shiny junction.
I strongly recommend searching online for soldering tutorials - I've run across several that explain the principles and techniques very well.
