Striding into 2013 ninth in the Premier League, a football great installed as their manager, preparing for their first ever League Cup semi-final against the moneyed power of Chelsea, there are endless opportunities for Swansea City supporters to pinch themselves. A popular choice is comparing the first three fixtures of this year – Sunday's 2-2 draw with Arsenal in the FA Cup, followed by Chelsea in the semi-final and Everton in the Premier League on Saturday – with the first three games of 2003. Ten years ago, with the club fighting to survive in the Football League's bottom division and only just saved from the threat of extinction under the ownership of Tony Petty, who bought the Swans for just £1, they lost 3-2 to Bury and 3-1 to York City then finally ended a run of six consecutive defeats by beating Lincoln City 1-0.

Another has been the reminiscences of Leon Britton, who first joined the club in December 2002 aged 20, and has since become the Swans' passing-rhythm metronome as they rose and flourished. Britton has recalled that when he arrived, on loan from West Ham United, an expression of the club's ambition then, the supporters' trust partly raised the money to pay his wages, rattling a bucket around the north bank on the old Vetch Field. Along with the eye-pleasing style of play, the hiring of Michael Laudrup as manager and classy summer signing Michu, this is another quality winning friends for Swansea: uniquely in a game sold to plutocrats, the same supporters' trust still owns 20% of the Premier League club.

Yet although in January 2013 Britton and Laudrup find themselves where they never imagined they would be a decade ago, the men who run Swansea do not exist in a state of permanent dazzlement by their achievement. They speak of greatly appreciating how good these times are, and vow repeatedly that the club will never sink back to any crisis like 2002, which is seared into all their memories. Huw Jenkins, a lifelong fan involved in saving the club then and now the chairman, explains their methods, their developed philosophy of football, in a way which seems grounded and quietly assured, not starstruck.

"We're all pretty down to earth, we come from quite humble backgrounds," says Jenkins, who used to run a Swansea building supplies company, of his fellow directors. "This is a run of games we could almost never have dreamed of 10 years ago, but there is no danger of us getting complacent. The most important thing: you have to have a clear vision of what you are doing."

He talks in that context about Swansea boldly signing Laudrup, rather than a candidate from the standard list of available managers, when FSG, Liverpool's American owners, decided Brendan Rodgers was their man for a new era at Anfield. "We decided that if we could find the right person at this stage, he would enhance our image and take us forward as a football club," Jenkins explains.

"Michael Laudrup is that person, he brings us that credibility. Firstly, though, he had to fit in with the parameters we set. We don't bring somebody in to run the club; we feel we have people doing that pretty well. He is here to coach the first team, to work with us."

Jenkins stresses that Swansea's striking emergence as the British team most wedded to a Spanish style of passing football was minted before the Spaniard, Roberto Martínez, arrived as the manager in 2007. The chairman gives credit to the discipline, shape and stability of purpose instilled by Kenny Jackett, who won the first promotion, from League Two, only eight seasons ago. Even in League One Swansea found themselves competing with the fallen giants of Leeds United and Nottingham Forest, understood they could never compete financially and bought into a playing style which might give them an edge. Jenkins argues that Martínez, Paulo Sousa briefly in 2009-10, Rodgers and now Laudrup have all developed their teams within that same approach, based on triangular passing, retaining possession, pressing, and striking quickly.

The philosophy, still wedded to taking care of the finances, extends to the selection of players – young men being offered their first taste of the Premier League, judged to be hungry for success. "Back with Kenny Jackett we could see what was needed to move the club forward," Jenkins says. "We had to get away from the typical British 4-4-2 formation and 6ft 2in players who run around a lot. Most clubs don't have a clear vision, they allow the manager to set the direction, then they change the manager so often, they get stuck in a merry-go-round. We had to go down a different route, to compete with clubs who think spending money is the only way to get success."

In their first Premier League season last year, Swansea made a profit of £14.6m, on the enormous £53m increase in income brought by promotion, from £11.7m in the Championship, to £65m. Even the promotions were achieved without a permanent training ground, a position now being rectified with two complexes being built, one in partnership with Swansea University. The club has also submitted plans to enlarge the Liberty Stadium, eventually to 32,000, to cater to current demand.

The wage bill, notoriously difficult to control in the Premier League, almost doubled, from £17.4m in 2010-11, which included the players' end-of-season promotion bonuses, to £34.6m last year. The players have a standard clause in their contracts for their wages to reduce were the club to be relegated, a necessary protection.

Jenkins is quite proud of Swansea's trading in the summer, a profit from the sales of Joe Allen, £15m to go to Liverpool with Rodgers, and Scott Sinclair, £6.2m to Manchester City, while Swansea signed Chico, Pablo Hernández, and, for just £2m from Rayo Vallecano, the stand-out languid talent of Michu. Swansea do intend to make two or three signings in January, although Jenkins is cagey about naming players Laudrup is considering.

Jenkins ascribes the loss-making financial whirlpool as the reason so many clubs are sold to overseas investors, including Cardiff City, now owned by Malaysians, while Swansea are owned by local people, and 20% by the supporters' trust, the envy of fans at many other clubs. "We all take pride in going against the norm, where clubs lose millions of pounds and need owners to pump money in," Jenkins says. "There is no need for it."

Huw Cooze, elected by the supporters' trust to serve as its director on the club's board, says that, with hindsight, the circumstances favoured the trust, allowing it to buy such a significant stake when the club was facing collapse. "It has worked out well for us and it keeps the club close to the supporters; we feel it is still our club," Cooze says. "Ten years ago we were down with the dead men, nearly out of the league. Now we hope Michael Laudrup can take us to another level. The feelgood factor in Swansea is huge, and, yes, we are all proud of our club."