How much time does it takes to buy a landing slot?
I know that in the Netherlands this procedure is open and not obscured behind a login portal.

In the Netherlands the commercial airports are operated by the Schiphol Group, the number of flight movements or slots per airport is determined in collaboration with the government. For Schiphol this is now 500,000 per year. The allocation of the slots is governed by a second body which is set up to be non discriminating in the allocation of slots. Most of the answers to your questions can be found there: https://slotcoordination.nl (English website)

Who allocates slots?


  Under the European Union rules – (EC) Regulation 95/93, as amended -,
  a Member State of the EU needs to appoint an airport coordinator for
  each coordinated airport. The same coordinator can be appointed for
  more than one airport. SACN has been appointed for coordinating AMS,
  EIN and RTM. Coordinators are independent bodies to maximise
  transparency.


How often are slots allocated?


  Slots are allocated for each season, and slot coordination recognises
  two different ones. There is a Winter season and a Summer season. The
  mark of the change of season coincides in the EU with the change of
  summer/winter time. The difference is recognised to make sure we use
  daylight optimally.


How are slots allocated?


  The allocation planning process starts around six months before the
  start of each season. Slots are allocated free of charge from a pool
  of available slots. Allocation takes place according to certain
  priority rules in a neutral, non-discriminatory and in a transparent
  manner. The leading principle of distribution is based on historical
  precedence, the so-called grandfather rights. When an airline operates
  a series of slots in a season for 80% or more, it can hold on to the
  same series in the next same season. When it operates less than 80% it
  loses its historic rights (the so called ‘use-it-or-loose-it’ rule).
  Slots can be re-allocated until the day of operation.


What happens when the requested slot is not available?


  An airline can keep its request on the list of ‘outstanding requests’
  to see if during the allocation process slots become available over
  time. Airlines can freely exchange slots. Prior to each season a
  worldwide Scheduling Conference takes place enabling face to face
  meetings between airlines, airports and coordinators to improve the
  allocation process.


Apart from being assigned a slot, an airline also needs to file a request with the airport to request for the required services to handle the aircraft. Schiphol has a very informative website with a lot of publicly available information:

For passenger handling (gates, check-in, etc.)

https://www.schiphol.nl/en/operations/page/passenger-process/

For aircraft handling (gate assignment procedure etc.) 

https://www.schiphol.nl/en/operations/page/aircraft-process/

If you want to know more about the trade in landing slots then I would suggest opening a new question since there is a lot to tell about that subject as there is a lively trade going on there.