Roger, if you look at your kit again you will see that a lot of it is self-explanatory.
Firstly, look at the "contents" section of the datasheet that came with the kit. Here you will see the listing of the parts and some clues as to how to identify them; the resistors have coloured bands that indicate their values. The circuit board is printed with the outlines of each component in blue; you just need to align each part with its outline on the board and then solder the pins underneath. If you look at the pictures on the website here,
http://www.picaxestore.com/index.php/en_gb/picaxe/project-boards/axe118.html it is helpful in getting it assembled.
Perhaps if you ask more specific questions we can help you more; in the meantime I have annotated a photograph of the board to give you some idea of what goes where and how. It is just a quickly assembled visual aid to get you going.
A couple of further notes;
The sockets for the integrated circuits are there to make sure that you don't damage the chips themselves when soldering. The downside is that the chips can be tricky to push into the sockets without damaging the pins. A little careful tweaking inwards of the pins on the chips will help to align them with the sockets. Above all, make sure that you respect the alignment indicated by the notches on the pictures, the chips and the sockets; that makes sure that everything is the right way round.
RPU and RPL may be confusing you; this stands for Resistor Pull UP and Resistor Pull DOWN. This determines how the switches work on the input side; you can wire the switch so that it connects the respective pin to 0v (negative or ground) when you click it or to +ve.
Which you choose may not matter much for a model railway signal; in some interfaces it is important.
Tell us where you are stumbling and the help will be here.
Edit; I see that while I was creating the picture for you there has been further posting. Tell me, what sort of model railway signals do you want to operate and how do you want to trigger them? That will help in advising whether to go for pull up or pull down.