I think that you should opt for n.O.e. diff spectra as suggested above by Gennaro. But please do not forget that one missing interactions are not good prove that the groups are not on the same side of olefin. Better to irradiate all possible hydrogens and to see what are the results.

The simplest way is to look for NOE signals. If you have a CH or CH2 or CH3 attached to each olefin carbon, you may see the NOE's between geminal and cis groups, but not trans ones.

You can also use RDC applications of NMR in anisotropic media

Article Weakly Oriented Liquid-Crystal NMR Solvents as a General Too...

Could you give me the name of the alkene ( I do not like to call olefin, as this old name is not recomented by IUPAC) ? In order to give some usefull suggestion it is important to have the compounds name (or formula). You may send me by e-mail.

IR Spectroscopy works well with substituted olefins.... For more details please refer Silverstein..

you can a APT NMR or Dept, in 13C, and differentiate carbons primary, secondary, tertiary and quaternary

U can try NOESY, A COSY will tell you which protons are adjacent to one another while a NOESY will tell you through space interactions whether that proton is close to in the molecule.

IR spectroscopy as suggested by Anan is limited in complex alquenes. RNM is much more powerfull as I discuss on my book "Espectroscopia no Infravermelhora na elucidação de compostos orgânicos". For full referecen see my Hope page at www.luizclaudiobarbosa.com.br .

I think that you should opt for n.O.e. diff spectra as suggested above by Gennaro. But please do not forget that one missing interactions are not good prove that the groups are not on the same side of olefin. Better to irradiate all possible hydrogens and to see what are the results.

HSQC, HMBC (connectivity) and NOE (spacial relationship)