For planetary combat the rules are similar to boarding parties. In most cases it won't be possible to take a planet (Earth, Mars, Vulcan, Romulus, etc) because the troop concentrations and populations are so large. However, small portions of such planets can be conquered and small planets, stations, moons can be captured.
If a station/moon/small planet has troops numbering 1000 then 1250 troops must be beamed/transported to the site. At the end of the fighting there would be 500 prisoners and 612 guards. These could be transported up and for two game days (1 day RT) the faction which has taken the installation can do with it what they will. If it's only a mine or such they can transport number of crew necessary to run it. IF, however, it's a small planet/moon with a population the conquering player must beam down a number of troops equal to 20% of the population to keep order. After 4 weeks RT the garrison can be reduced to 10% of the population. After another 4 weeks RT a garrison will no longer be necessary to maintain order and the planet now belongs to the faction.
If a factions planet is taken and the factions retakes it in the first 4 weeks RT it is automatically loyal to it's previous owner. If they do it in the second 4 week period they'll have to station 10% of the population in troops because some of the populous has changed loyalty to the other side. If it's after the entire 8 week period they must station 20% of the population in troops and do the reversion of loyalty.
So if a population of 20,000 exists then 4,000 troops must be stationed for 4 weeks RT. In the second 4 weeks RT only 2,000 troops would have to be stationed. And after all 8 weeks no further troops would have to be stationed (Though you might want to leave troops to protect the newly taken planet).
Bombarding a planet is also possible. Installations such as mines, research stations, manufacturing plants, etc can be bombarded from orbit and destroyed.
Military organizations and troop concentrations can also be bombarded. For every point of weapon damage 100 troops are killed. If the troops are near population centers then 500 civilians are also killed. So a phaser beam of 8 power fired into a military installation near a population center would kill 800 troops and 4,000 civilians.
Population bombardments are also possible. For every point of damage done to a population center causes 1000 deaths. So an 8 damage phaser beam would cause 8,000 civilian deaths.
If any civilians are killed in a bombardment then any eventual troop garrisons must be doubled since the population is much more hostile. So if a 24,000 population moon is hit with a 4 point beam killing 4,000 civilians it would leave 20,000 people that needed a garrison which would look like this:
First 4 weeks: 40% of population in troops to maintain order. So for 20,000 people it would take 8,000 troops.
Second 4 weeks: 20% of population in troops to maintain order. So for 20,000 people it would take 4,000 troops.
Third and final 4 weeks: 10% of population in troops to maintain order. So for 20,000 people it would take 2,000 troops.
*Note this garrison table is only needed for planets where civilians where slain in bombardment.*