Given assumed valencies: H=1, N=3, & C=4 i am now required to draw the structural formulae of HYDROGEN CYANIDE and CYANOGEN.

Question

H:C:::N is the Lewis electron dot structure. If you want to use "sticks" as a bond instead of two electrons, one stick stands for two electrons.
H-CtriplebondN. Note that H has one stick, C has four(one to H and three to N) and N has three (all to C). In this drawing, one stick is one valence.

I omitted a pair of electons for the dot structure on N. There should be a total of 10 (1 for H, 4 for C, and 5 for N = 1+4+5=10). Should be H:C:::N:
Sorry about that.

Wrong kind of structure.... is there another structural formula besides the lewis?

The stick and Lewis dot are the only two I know. I gave instuctions on how to draw the stick from the dots because it's difficult to do on the computer. Perhaps I can get some of it done and you will see how to do the remainder. In essence, however, you simply replace two dots with a line.
H-C=N. I can't put but two lines between C and N. You need to place another line there so there are three lines between C and N. To justify the lines with the problem (1 valence for H, 4 for C and 3 for N), you can point out that H has one line, C has 4 (one to H and three to N) and N has three (all to the C), thus satisfying the valence of all three atoms. We sometimes draw three dimensional structures but that is way outside the capabilities of this computer (and operator). However, I don't think for a beginning course that the teacher would be asking for that, at least not this early in the course.