Is my paper under review (or similar) for too long and if yes, how should I react?
How can I decide whether my suspicion is correct? What handling times should I expect?


First note that there is no general answer to this as average reviewing times vary widely between fields and even within a field.
Therefore, you need to resort to the following:


Read the documentation about approximate times on the journal’s website.
Look at some sample articles – at the dates of submission/revision/resubmission/acceptance that are on the articles – this gives you a bit of a guide. It is potentially more useful to to look at these details on an article similar to the one you submitted or are intending to submit.
Ask colleagues who are experienced with publishing in that journal or at least your particular subfield.
Familiarise yourself with the general workflow of academic journals.


  Given some expected handling times, when should I act? How much leeway should I give?



Check if there have been any holidays etc. since the submission. 
Send an inquiry about a fortnight to a month after the timeframe determined in the first step.  But this time can vary – it is a bit of a judgement call, depending on the timeframe that is stipulated and the amount of time that has passed.
Keep in mind that the main reason why peer reviews take so long is not the time required by the review itself but that the referee has to find time amongst their other duties (see also this question). Therefore review durations are subject to high variability.
Additionally, before you take any action, be sure to check the status of the submission. There is little point in nagging the editor if the status tells you that some progress was made recently, e.g., the reports have just arrived or a new reviewer was appointed.


  How should I act? Whom should I contact and what should I (roughly) write?


Send a polite email to the editor assigned to my manuscript – after the introductory pleasantries, politely get to the point, asking something along the lines of:


  I am inquiring about the status of the manuscript [title], as X months have passed, which is considerably longer than the Y months stated on the journal’s website.


Then sign off, thanking the editor for their time and the usual closing pleasantries.