At some point, I plan to make a comprehensive tutorial for randomly generating planetary systems, but for now have this:
How to generate some VERY BASIC parameters for a planet using dice: Note: D% gives a result of 0.00-0.99 inclusive.
Semi-major axis: 10^(4D%-2) AU. This will generate distances from 0.01 AU (near the roche limit of most stars) to 100 AU. This formula works for binary companions as well as planets. However, for very distance binaries (and a few planets) you may want to add an extra 2D%. About half of the planets generated by this method will be within 1 AU and half will be beyond 1 AU. If you want, you can multiply the result by the square root of the star's luminosity to get a similar proportion of "hot" and "cold" planets.
Planet type:
D100:
1= Gas Dwarf:
2-30= Rock Dwarf:
31-60= Ice Dwarf:
61-80= Ice Giant:
81-99= Gas Giant:
100= Rock Giant:
This may not reflect the actual frequencies of planets. Note that this is not based on distance. However, it seems to be more common to find icy and gaseous planets inside the frost line than rocky planets outside the frost line. Also note that extremely hot ice or gas planets may lose their outer layers and end up as cthonian planets. The lighter and less dense the planet, the more vulnerable it is to this happening.
Planet mass:
Gas Dwarf: M= 10^(1D%) Earths.
Rock or Ice dwarf: M= 10^(3D% -2) Earths.
Ice Giant: M= 10^(1D% + 1) Earths, upper limit 50 earths.
Gas Giant: M= 10^(3D%+1) Earths, lower limit 25 earths, upper limit 4000 earths.
For gas dwarfs, this will generate mass between 1 and 10 earths. I'm not sure smaller gas planets would be able to hold themselves together in the inner regions of the system (and ones further out would probably grow).
Rock or ice dwarfs go from about the mass of the moon to large "super-earths". Ice and gas giants range from neptune-sized to the deuterium fusion limit.
Your planets density will be dependent on its composition (rock is more dense than gas), its mass (gravity compresses most substances, which means that a 0.05 earth mass planet will be less dense than a 5 earth mass planet of the same composition), and temperature (see "puffy planets." to a lesser extent ice dwarfs may get hot enough to boil and puff up). For superjovians you typically want to generate a diameter (between 130,000 and 140,000 km) instead of a density. For puffy planets generate a bigger radius.
Orbital inclination and eccentricity can be based on many factors, including tides and orbital resonances. It's good to think carefully about how a large planet's gravity will affect the rest of the system.
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