The process for removing a non-paying tenant from a property has been changed by Ley 37/2011 which attempts to speed-up the process.
While it has certainly improved the legal process, the under-resourced court system still constitutes an impediment to a truly fast system. In any case, the process is as follows:
Notice to Quit
Once the rent has fallen due and is unpaid, the landlord should present a demand to the tenant that the outstanding rent be paid (usually by burofax available in the post office which is proof that it was sent on a particular date).
The reason for doing this is that it allows for the possibility of the tenant leaving the property without having to go through the legal process and the expense involved in hiring a solicitor, court taxes etc. Where the tenant voluntarily leaves the property is probably the best possible outcome in most cases, at least from the point of view of legal costs.