From the balcony at Valdebebas you can see for miles. To one side stands the new terminal at Barajas airport with its huge bamboo frame. Further round, the sierra rises up, bordering Madrid to the north and west, snow settling on the peaks. And towards the city, Figo, Zidane, Ronaldo and Beckham tower above everything –the nicknames given to the four skyscrapers constructed on Real Madrid's former training ground – while below, maybe 10 metres down, lie the immaculate pitches where Real Madrid train now. And from here, Paul Clement smiles, looking right, you can just about make out his new house, too.

It has been some journey. The pitches are empty but not for long. It's mid-afternoon and training begins in little under an hour. Cristiano Ronaldo and Gareth Bale will be joined by Xabi Alonso and Isco, Karim Benzema and Iker Casillas. Clement will be in the middle, leading them. The son of the QPR player Dave Clement but never a professional himself, Paul Clement is the Londoner who followed Carlo Ancelotti from Chelsea to Paris Saint-Germain, where he worked with Zlatan Ibrahimovic. Now he's assistant coach at the biggest club in the world, alongside Zinedine Zidane.

"There were a couple of opportunities, including one abroad and one in the Championship," he admits. "But I was really excited about coming here. It's an ambition [to be head coach] but I'll stay here as long as I can. It's a great experience to work at this level: it's the pinnacle."

It's hard to disagree: in Monday's Champions League draw, no one will want Madrid, who finished on 16 points, having scored 20 goals in six games with Cristiano Ronaldo getting a record nine goals in the group phase. Since losing the clásico, Madrid have scored 24 in five league games. But it is right here, on these pitches, that the difference really strikes Madrid's English coach.

"I can think of one particular exercise we've done at all three clubs. The players were doing it here very early on, and myself and Carlo just looked at each other. We couldn't believe the level," Clement says, his tone conveying the impact. "Chelsea had fantastic players but they were different: mature, powerful, very strong physically. Paris Saint-Germain had a mix of the old PSG and the new, and Ibra would do things that were just unbelievable, things I've never, ever seen before, but there was a big range. Here, from young players to old, the technique is so good. The thing I noticed from day one was that the execution is at a higher level. Much higher.

"You have to keep challenging them, so you reduce time and space so that they have to think quicker, act quicker."

That ability is especially evident at Madrid but Clement believes it runs throughout the Spanish game. "When you go down to teams in 18th, 19th or 20th they all try to play, they have good creative players: wingers, players off the front. There's a higher technical level than the lower levels in England and in France as well."

Is there an explanation for that? Clement ponders. "I think it's a cultural thing, a belief in a certain way of playing. You see it in the national team and the academies. At seven or eight, they're already developing two-footedness, they're not so concerned about the physical side or winning. They believed in that and now they're reaping the rewards. English clubs are now more interested in that [approach] and are working hard to improve but it is a long process."

It is a process Clement has seen with different eyes, having embarked on a coaching career from the age of 23 and taken the opportunity to work abroad with Ancelotti. He concedes that he might have been offered jobs sooner had he played but would not necessarily have been a better coach. "Signing ex-players is a safer bet in terms of the pressure, but the thing about playing is you're often thinking about yourself; when you're learning to be a coach you are thinking about bigger things and I have been doing that for a long time now." Instead, he has watched, studied, and developed.

Much is said about the result of the work players undertake; rather less is said about the work itself. Clement believes in "open, attractive football", with the emphasis on intelligence and technique, even as he accepts that it carries some risks: the short blanket theory. As he explains the mechanisms, the methods and ideas that underpin what he, Carlo Ancelotti and their players actually do, the drills and the lessons, it's clear that these are processes that have been thought and re-thought, discussed, applied and adapted over time; it's clear too that Clement believes in coaching.

Yet the knowledge is worn lightly and presented simply; there is no mystification of the manager and no possessiveness. He says it's natural to watch England games, for example, and wonder what he'd change, who he'd play. But asked what he would do in Roy Hodgson's position he laughs a laugh that says "nice try" and responds: "Roy's doing a great job." He talks naturally about shifting Madrid's shape from 4-4-2 to 4-3-3 and 4-2-3-1 depending on the players available; about the discussions that led them to their current formation. And about what the daily work entails.

"Today, for example, because the players have had two days off we won't work hard," he explains. "The old style in England would be the first day in after a day off you'd kill the players, but there's more knowledge about how to train effectively now. What we do is conditioned by and focused on the next game, aided by the work from the scouting team which you incorporate as quickly as possible.

"You work from the game and come backwards to the sessions. You don't invent things for the sake of it. All the drills, even the warm ups, which are always with the ball, emphasize good control and passing: diagonal passing. Not playing straight, not playing lateral; always an open body position, trying to play forward, playing on angles.

"But football is not complicated; it's simple. We don't make up things. It's not a circus. We try to keep things simple and related to the game. Coaches like to be guarded and I certainly wouldn't put my set plays up in the opposition's dressing room but I'm not sure there are that many secrets. Take set plays: when you're defending: individual marking, it's your responsibility. When you're attacking, I always say to the players: 'guys, it's about the ball you put in'.

"At this high level, it's about the little marginal gains, whether that's having an excellent nutritionist or someone to help recovery: those things can make a difference. That's down to both the players and the club."

Ronaldo is the obvious example. "Cristiano's a senior player and has had a great upbringing, working under Ferguson," Clement agrees. "He's at a stage of his career where he's made mistakes and learned and he manages himself really well. There was a game we arrived back from at 3am and he went off for an ice bath. Another time, we got back from Istanbul at 6am and the physio's giving him a rub down." You might be thinking that it's the physio you feel sorry for. Clement laughs: "Yeah exactly. He's alright, he's just got to lie there!"

"As for Gareth [Bale], what I like about him is that he's down-to-earth in the dressing room," the Englishman continues. "He's quiet, he's humble. On the training field he knuckles down. He's young still so it's very exciting. He's coachable ..."

Coachable? Are there players who aren't? "Oh yeah, without doubt," Clement grins. "Gareth wants to improve. A couple of games ago, he got into good scoring positions and wasn't finishing. So the next day he says: 'can we do extra shooting?' After training, he's one of the last to leave, whether it's having additional treatment, the gym, or ice baths. His food is right. He's a very, very good professional. In my experience of working with players like Frank [Lampard], John [Terry], or Ashley Cole at Chelsea, Zlatan at PSG, or Cristiano or Gareth here, what stands out is that they are top professionals. They have the talent but they do all those other things that make the difference."

Some have seen in Bale a clone of Ronaldo. "Do you think so?" Clement asks. There is surprise in his voice. "Cristiano's an incredible player: at the moment in my opinion the best there is in the world. Listen, there are similarities, no question: both are good with dead balls, both are wingers who score an incredible amount of goals, both are athletes ... but I think Gareth comes in between the lines more. Cristiano is very direct in his style, whereas Gareth will come inside and play combinations. He'll look to slide balls into others. Ronaldo is very direct.

"Football is simple: there is a goal and you have got to try to put the ball in it. And I think that's exactly what Cristiano thinks."