Mourinho's teams are always known for their organization at the back. Mourinho will be happy to win  any match 1-0 than 3-2, that's him. Mourinho feels that, "The one who has the ball has more pressure", " IF you don't concede the goal, you'll have more chances to win".  His teams Porto, Chelsea and Inter Milan all were good defensively and relied on counter attack. Give him a set of players who will do, whatever he asks them to do, there's no better manager than him.
As I don't know know about his tenure at Porto, I 'll get started with Mourinho's tenure at Chelsea. Chelsea won the first PL in 40,50 years(with many games won by them 1-0). They had Terry, Makelele etc renowned players back then, but Mourinho had a problem when he faced Liverpool in the CL as Liverpool then had Rafa Benitez, who also plays 4-2-3-1.A stable formation, a safe one(Rafa is more defensive than people think) Liverpool with their fans behind can give headaches to many teams, even with much weaker side.  Benitez's defensive tactics cancelled out Mourinho's tactics.So, he couldn't beat Liverpool in the CL.

  During his tenure at  Inter milan, he was pretty successful. Inter Milan won a treble in his last year. Italian teams are known for their  superiority in defense .They may be boring to watch, but teams in Serie A are  tactically astute. This was the ideal place for a coach like Mourinho( A coach who relies more on his team's defense more than attack).   His team triumphed against every team. Defensive Masterclass was shown against Barcelona along with some luck in the Camp Nou and they eventually won the CL by beating Bayern Munich.

    Mourinho came to Real Madrid after his successful tenure at Inter milan. His defensive strategy was of less use in the La Liga. Also, Real madrid  nicknamed as "Los Galacticos" demanded a particular style of play. They need to WIN WITH STYLE , to close down the space in terms of Superiority between their bitter rivals FC Barcelona (who were regarded as the best team and were winning almost everything that was in the sight.)
  Mourinho had to change his tactics. Real Madrid got slaughtered by Barcelona due to their style of play in the epic, historical 5-0 thrashing by their greatest rivals . Even though they played well after that, Barcelona were at their highest peak. Barcelona eventually won 2010-11 La Liga and CL. Mourinho had finally beaten Barcelona using some of his old tactics in the CDR final(Defensive tactics).

Mourinho finally beat Barcelona in the La Liga race during his second season at Madrid, but failed to beat Bayern Munich in the semis of CL. Pep Guardiola could have stuck with usual 4-3-3, but he was experimenting too much with the formations during 11-12. Thus Barça were able to win just Copa Del Rey during 11-12.


How Real Madrid play?

 When REAL MADRID BUILD AN ATTACK from the back. You may think Xabi alonso drifts front, but that's not the case . Xabi alonso occupies the Ramos space and Ramos moves front.

 During counter attack, The long passes are sent by Alonso to Cristiano Ronaldo or Di maria. And in order to win the La Liga, you have to win almost every match as Barcelona wins every match.So, Real Madrid had to play higher up the pitch  and Mourinho is weaker in the final third. They did face many problems in the away games where the opposition were happy to park the bus. Also  Pepe and Ramos getting frequent Red cards didn't help either. If you recall Real Madrid vs Manutd , Manutd were happy to defend (Mourinho's strength) and  Real Madrid had to play higher up the pitch and they looked totally hopeless, without having any idea."Give the ball to Real Madrid and they don't know what to do with that."

   For all hype about Xabi Alonso, he is very slow and is the weak link in the Madrid's side. Messi has owned him every match. He cannot even tackle properly, Mourinho brought Luka Modric into the team to have a control over the match. Because they already had Khedira as a DM. Xabi Alonso and Khedira are two DM's and do not offer any threat in the attack(When oppositions park the bus, these two players are hopeless. Modric is a bigger threat in that aspect)

 Thanks to Nani's red card which created havoc in the Manutd side and a clever substitution by Mourinho to bring Modric in, which led Madrid to win the tie and go through to the next round.Even Galatasaray were able to break   Madrid' s defense involving Varane, Pepe and Ramos. Madrid always had a problem when teams play high tempo game. Guardiola' s Barcelona were impressive in every game against Madrid. The 1-3 win was the proof of Barcelona's superiority in terms of quality and tactics. Well leaving that behind, Borussia Dortmund slaughtered Real madrid  again after having triumphed earlier in the group stages. Against Dortmund, Varane played as a CB(Not experienced). Ramos played as RB. Jurgen Klopp knew how to close down Alonso(weak link) and  they successfully closed down Xabi Alonso in the knockout match.   Borussia Dortmund were hammering them throughout the game  with their high tempo display. Real  madrid  eventually went  out of the  CL for the third consecutive time.

As far as the league is concerned , Barcelona had not lost a single match in the first half of the season and Real madrid  had no hope. Mourinho's obsession was/is  CL and Barcelona.

Jose Mourinho's Real Madrid was very successful in knocking out FC Barcelona in 2012-13 Copa Del Rey. In the first leg, the score was 1-1. Cesc Fabregas and Pedro missed shit load of chances to kick Real Madrid out of CDR, but they didn't. Meanwhile, Mourinho had figured out the weak links in the Barca team. The space left by the two full backs of Barcelona i.e Alba and Alves was used effectively by Real Madrid. He won 2 consecutive games against Barcelona using this tactics. He eventually built a team  which could beat Barcelona by making them a BEST COUNTER ATTACKING TEAM,  but failed to win anything in the last season  even with such top squad, with LOS GALACTICOS, due to his over obsession with the Barcelona. You can read Sid Lowe's book to know more about Mourniho's tenure at Real Madrid. The counter attacking teams will be the least favorite to win the league. Want an example? Chelsea FC.

Summary

 Mourinho relies on counter attack and good defending at the back, but both Ramos and Pepe let him down in the big games.

Mourinho relied on Xabi Alonso too much. He is the biggest weakness in the Real Madrid's side IMO. He tried to change it by introducing Modric more often, but it was too late.

Mourinho's obsession with Barcelona. He wanted to beat them, that's it. If you do not know till now, Mourinho is all about himself(SMUG). Just look at his press conferences, "Mourinho: I never lost at Stamford Bridge." "Mourinho: I never went out of CL QF" etc. He loathes Barcelona and Barcelona were too good to lose to him and won most number of times against Real Madrid during his tenure.

Controversies.

1) Benching Benzema( Perez's favorite) and demanding another striker. Adebayor came to Madrid just because Mourinho didn't like Benzema.
2) Poking Tito vilanova in the eye
3) Making Absurd comments on Barcelona
4) Players at Real Madrid didn't love him as they did in other clubs
5) Benching Iker Casillas was the biggest mistake, he was Madridistas favorite
6) Mourinho tarnished Real Madrid's image during his tenure at Real Madrid and went out in ugly fashion  by losing to Atletico Madrid at Bernabeu..


The first season where he went trophy less was in the spain, "A two Horse Race"

Photo credits : Thore haugstad (http://www.Haugstadfootball.net)