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Template.pdf should be the same as the .pdf output when you “compile” the NC2026_Paper_Template_Latex.tex file.  I suggest that you try compiling this first to see that you have everything necessary in your version of Latex to have it compile.  Compare your output .pdf file with the result in Template.pdf (What I got when I compiled NC2026_Paper_Temple_Latex.tex renamed to Template.pdf).  You should check that the bibtex part works, too, by renaming the .bbl file and using the bibtex compiler.  The references for the template are in sample.bib.    That is how I created the .bbl file.   Check the .pdf output to make sure all the referencing is complete.  Note (for people new to Latex) that this often requires several runs of the compilation of the document for Latex to get the references correct.   
Once everything is compiling properly, now start on your paper.   

Copy the NC2026_Paper_Template_Latex.tex to NC_2026_YYYY.tex, where YYYY is your abstract submission number, with zeros in front if the number is less than 4 digits, e.g., if your abstract submission number is 152, you filename should be NC_2026_0152.tex.  
I suggest you start by editing this file to create your paper, leaving the template .tex file alone for reference. Note again that YYYY stands for your abstract submission reference number.  