There are many factors that go into planet/celestial-object creation. One of the more problematic is that as the mass of an object (and, therefore, it's gravitational influence) increases, the size of the band of space around the planet that it "sweeps clean" increases. Thus, as planets/bodies form, there are places where other planets could form... and places where they can't.
A consequence of this problem is that you could have a lot of little celestial bodies or a few large celestial bodies... but it's hard to have both.
1. Make the radius of the initial proto-planetary disk very large
From a practical (and very simplified) point of view, you can't have a celestial body where there isn't any mass to allow it to grow. Since each celestial body requires its own space, you need to provide the space necessary for the number of bodies you want. Thus, the proto-planetary disk must have a large radius.
2. You need a big enough star
Think about a planet and its sun like a tether ball and the pole that ball is tied to. The weaker the pole, the smaller (less mass) the ball must be or the pole tips over. Gravity kinda works the same way. Your star is a big, firm pole well cemented into the ground — and the more true that is, the more total mass can swing around it. Unless you count boulders, rocks, and rubble as "bodies," you need a large star for a large number of bodies.
This has consequences I'm blatantly ignoring, like increasing the distance between the first planet and the star, causing more heat on more planets further from the star, and having a tremendous effect on the orbital speed of planets. Not to mention that the greater the star's gravity, the greater the relativistic effects on the planets. Yup... I'm ignoring all of that an quite a bit more. Praise Glarnak for the science-fiction tag.
3. Which means you need, conveniently, a distribution of mass in the proto-planetary disk that has greater density in the center and rapidly thins out to a uniform density toward the rim
This is pure worldbuilding. The entirely circumstantial convenience of having enough mass at the center of the proto-planetary disk to create a large star and just enough mass everywhere else to create all the planets you want in the way you want to create them. In other words, we're not talking about rules that could be universally applied throughout your universe, but rules that can be conveniently applied to a single star system. But... who's to say your universe doesn't conveniently clump stuff together like this?
4. Ignore chaos theory
This, unfortunately, is the really big elephant in the room. Chaos theory basically states (and angels just began weeping, did you hear them?) that crap happens. Crap... not roses... which also happen, but not as often as crap. Not by a long shot. What this means is that the probability of getting the kind of system you want is vanishingly small in Real Life. Praise Glarnak a second time for that science-fiction tag.
5. Add mass during the formation process
Finally, consider the improbable-but-not-impossible condition of two colliding clouds. One is your proto-planetary disk. The other, conveniently perpendicular to your disk, is a stringy cloud of extra mass that trundles along at a slow enough rate that it provides the extra mass you need to create a bunch of planets at, basically (get more kleenex for those angels...) minimum distance-between-planets conditions.
Conclusion
Writing a story involving the kind of star system you're talking about means declaring the existence of the star system "to be so" and using information like what I've provided to lightly and gently rationalize the existence of the system. The last thing you want to do is provide a lot of detail about how that system formed. The more detail you try to add, the more holes you're handing the reader to poke their fingers through.
And just because offending the god of Worldbuilding is a bad thing... praise Glarnak.
