Depends on what you want to say about your SAM; besides what others suggested, you can use electrochemical techniques, as well, such as cyclic voltammetry and impedance.
Although this is an indirect approach, if your monolayer is reactive, are there any protocols to reliably deposit a flourescent or other contrast agent? For example, we get a good sense of our monolayers based on the self-assembly of gold nanoparticles. This is indirect, but works if you don't have access to some ofther tools mentioned in the other answers.
In addition to spectroscopic techniques (ATR-FTIR, PMIRRAS, electroreflectance, SPR) you can use Quartz Crystal Microbalance as quartz crystals usually have a gold layer. With these technique you can determine the amount of mass deposited. Also, you can perform electrochemical experiments with these crystals.
FTIR (ATR and specular reflection, IRRAS) - modification is present
AFM/STM - visualization of Au111, ~300 nm flar domains with SAM
SEM may also work but you won't get to the resolution of AFM.
QCM- quantification of amount of SAM on the surface
Ellipsometry - gives you thickness of the SAM. You can use it to calculate tilt angle of the monolayer on Au since it will never be perpendicular. Octadecylthiol has a tilt angle of about 8 deg.
Using FTIR you can also monitor the formation of SAM if you want to get really fancy. This is actually pretty cool, as you can determine the time when your SAM is formed.
Grazing Incidence X-Ray Fluorescence might also be of help. If you have a marker element in your head group, you can use that to learn about bonding angles, surface coverage and so on. We do such things from time to time. Check my publications and feel free to ask questions if youre interested to learn more.