Basically there are 3 components to a Montessori class so, you can break the observation down into 3 categories, if this helps.
1. The Children: if its Children's Home or "Casa" the ages will be between 2 1/2 and 6+. Toddlers are 1 1/2 to 2 1/2, Elementary is 6-12, often separated into 6-9 and 9-12, Middle school or High school. Observe the overall "tone" of the class: it should be unhurried, with children at work, focusing and also with some who have cleaned up and are going to find something to do next, some may be eating snack or doing art work or singing songs but in general, there is a general calm - projected by the adults and certainly, by this time of year, expressed by the children. Hopefully, you'll see children helping other children, older children teaching lessons and helping out.
2. The "Prepared" Environment: low shelving and fixtures, activities within the child's reach and proportionate to their body, made of natural materials. A full set of Montessori didactic materials include Practical life (care of self, others, the environment, social graces), Sensorial, Language (includes Spoken Language) and Math. You should see a Pink Tower, a bead cabinet, Metal insets with pencils and paper, moveable alphabets, fraction insets and many more. Low windows, natural tones for walls and floor, access to the outdoors (ideally a free flow in and out), a water source, also a one or two class pets.
3. A "Prepared" Adult: look for adults who are in attuned to the entire class while showing clear demonstrations to children, at their level...someone who speaks in low voice tones...someone who is gentle yet firm...
more later wigam.
Good luck!
Let us know how it goes...