Some champions are ineligible for skins because they are waiting VGU, this champion will only get a skin if said skin is already developed or woudl result on little effort/time for the team. Example of said skins are Debonair Galio. This sort of skins are the exemption not the rule.
If the champion is eligible for skin then is up to the creative team to decide what champion they are going to brainstorm a skin idea for. Usually on this phase they brainstorm a skin for 10 different champions or so and then decide which champion/skin combination they want to follow, this is usually the way most skin came to.
Some times, they have a topic, said Maruder or Pool Party and with that idea they brainstorm what champions they should be able to fit into that theme.
The reason why some champions have more skins than other is popularity, when the 10 champions/skin ideas is first presented is presented to an outside board that will calculate profit into the equation but also the developer themselves are players (most of them are anyway) so their vision is a tad bias towards whatever champion they main making them sometimes push some champions into getting skins, take for example Dr. Mundo, he is a champion with only 2.8% popularity yet he has gotten a skin per year for the last 2 years so I'm pretty sure someone on the development team mains Mundo. Also Skarner (the guardians of the sand skin) was conceived on similar way since that skin was redundant on him which his lore ties him back to Shurima and the skin seems redundant (since Riot has said they like to put champion on a different timeline or dimension so is not redundant)