You cannot book stopover tickets online. You have to call.
As stated above, you can only have a stopover on a return booking; and only in one direction (either the outbound or the inbound; you cannot stopover on both). It should not increase the cost of the flight; however, it may very well do, depending on the availability on the sectors necessary to complete your travel. (Flying Blue proces are now "starting from" prices - so even a direct, non-stop routing between origin and destination without any stops may not be possible at the advertised price).
A stopover is a deliberate break in your journey of over 24 hours. Necessary stops of less than 24 hours to connect points that have no direct service are, of course, always allowed.
A stopover can only occur where it makes sense, i.e. Where it occurs at a logical break in your proposed journey. So a stopover in MSP on LHR - ANC would appear OK (though presumably this would require an Alaska Airlines segment which may cause problems) while a stopover in Bangkok on a London to New York ticket would clearly NOT be OK. The same logic as for selecting transfer points should apply here...which can be paraphrased as not going unnecessarily out of the way, or require the addition of several otherwise unnecessary segments in order to complete travel between all listed points (origin, stopover, destination).
Just pick up the phone and talk to a Flying Blue agent.