What is the electron-dot structure of the covalent compound that contains one nitrogen atom, one hydrogen atom, and one carbon atom?

So, the compound is HCN.

H can only form one bond, while carbon can form 4 bonds and N can form three bons.

That drives you to conclude that H will bond the carbon and the carbon will form a triple bond with N:

H - C (triple bond) N

Now, you must count the valence electrons to determine how many and where valence electrons are not forming bonds.

H has one valence electron which is in the H - C bond.

C has four valence electrons which are one in the H - C bond and three in the CN bonds.

N has five valence electrons and it has three of them in the CN bonds, therefore you have to add two electrons (points or other marks) to the N atom.

This is the resultant Lewis structrue:

                               **
H - C (triple bond) N    (draw the two ** close to the N symbol)

You have to draw three hyphens to represent the triple bond and include the two ** over the N atom to represent the two electrons that are not forming a bond.