How do I determine bond length(s) for a molecule?

If you wish to truly calculate bond length... you may want to look into using computational software like MolPro, or Psi4, which run user-written scripts, run from the command line (e.g. Windows Command Prompt, Linux Terminal, etc).

Or, you could do it the easy way and look them up on NIST and see if they have what you're looking for.

http://cccbdb.nist.gov/expbondlengths1.asp

To calculate it using MolPro, you would have to write a script for your molecule. Let's say we looked at #"NH"_3#. The script I wrote for that when first learning the software was:

#"geometry={"#
#"N"#
#"H1,N,Rnh"#
#"H2,N,Rnh,H1,Ahnh"#
#"H3,N,Rnh,H1,Ahnh,H2,120"#
#"}"#
#"Rnh=1.012 Ang"#
#"Ahnh=106.67 Degree"#

#"basis=cc-pVTZ"# #color(red)(" !correlation-consistent polarized")#
#color(red)("Valence Triple Zeta basis set")#

#"rhf"# #color(red)("!restricted hartree-fock, closed shell nh3")#

#"optg"# #color(red)("!optimize geometry")#

where #"Rnh"# is the initial guess of the bond length and #"optg"# optimizes the geometry to find the correct bond lengths and angles. (Note that MolPro does not understand the correct symmetry of #"NH"_3#, and one of the #"N"-"H"# bonds is bent inwards a little.)

Or, you could look at NIST and find that it is #1.012# Angstroms for #"NH"_3#.