Citzenship - or Naturalisation (to give it its other name) - takes 3 years to obtain under 'Old Rules' (i.e. those in force prior to July 2012)
But holders of a Spousal Visa must go through the whole gamut ... and so your wife's next move will be to apply for what is called 'Indefinite Leave to Remain' (commonly referred to as ILR).
ILR (under Old Rules) can be applied for - at the earliest - 28 days before the date on which your wife has been in the UK for 2 years; e.g., supposing her current visa expires on August 15, 2015 ... then she'd be eligible to apply anytime after July 19 next year - providing she had passed the 'Life in the UK Test' and also attained the required standard of Listening & Speaking by an approved Home Office Examining Body in the English Language.
However, in cases of Spouse Visas granted AFTER 9 July, 2012 - when the system changed and the so~called 'New Rules' became operable - then it will take longer to complete the Immigration journey.
Here, then, is an example of the timetable for those on the longer stretch - based on the present setup:
Arrival in UK: 13 September 2015; apply for Further Leave to Remain 21/2 yrs - 28 days prior to [at the earliest] and certainly before the visa expiry date of 12 March 2018 - then again for an extended 30 months to cover the period to 12th Sept'r 2020 = a total of 5 years for *ILR ... and THEN ... finally, once *that penultimate hurdle is over, foreign nationals can, if they so wish, apply for British Citizenship.
Phew!
Now, I ought to conclude by stating that the facts I've provided above are taken purely "off the top of my head" and should be regarded as a generalisation, as it were ... because I brought my wife to the UK away back in 2009 - at which point, the whole shebang was a lot more straightforward. Accordingly, I would offer my apologies for any inadvertent inaccuracies on my part.![]()