How do you play with rich sims??

Like most others have said I don't change up what my rich sims do from what other sims do, they just have more money and less worry. I focus on socialization a bit more in wealthier households because I can afford to. Otherwise I'm still building skills and making money off those skills (usually). I like drama so I often have affairs. It's easier if you have a lot of money, but also adds a bit of a challenge depending upon who your sims is going after.

Well, depends on how much imagination you are ready to invest in your game :)
I focus on what rich people often do irl: staying famous, gaining political power, charity.
So I choose such careers as Business and Politics mostly + social media and media production for younger ones.
Throwing parties to mingle with other rich and famous, charity events etc.
Donating items for fame (Get Famous perk) or just giving away money to poor household via gift option.
Some family members become these eccentric rich who collect rare collectibles.
Some artsy ones become Patrons of the Arts and build/improve museums and libraries.
Being rich doesn't mean they have to do nothing, on the contrary, they have power to make the world a better/worse place.
Well, mine are always goody two shoes, I'm boring like that :)
Can be a Criminal Boss or Villain just as well.

When I have rich families they still do things... still might have a job, or make money in other ways. They don't need to be rich to do this but basically they do whatever comes up that is personal to the interests (and changing interests) of that sim. Whether rich or poor I still have painters, gardeners, lotharios, aspiration doers, they go on vacations and basically any/everywhere.
The good thing about having or playing a rich sim is it is all at their fingertips.
If they are good they might give away money if bad they might find a way to swindle or marry into more. Give them a story and go!

I did want to add don't kick yourself if you can't enjoy playing like this. For now you might need the challenge of making them get ahead that is basically forced on you with little money. You might also need the time/need management to make you feel like your engaged. It's okay not to enjoy playing like that.

I play them like any other sim. They do aspirations, work on skills, most of them have careers unless they are working at home (painting or writing). The only difference is they are able to help those who are less fortunate.

Well, for me the sims is all about storytelling and families/characters. I also enjoy working on skills, careers and aspirations regardless of wealth. I don't usually focus much on making money anyway, although I do tend to prefer playing families with average incomes. I do have one rich family I'm rather fond of. The head of the family is an infamous vampire criminal boss and now rules over the vampires and the worlds, so his family lives in luxury and never has to worry about money. What makes them fun to play is the antics they get up to, the relationship/family dramas and interactions, and philosophical struggles the characters face. For example, I have plans for the daughter to have a son with a werewolf enemy (if/when we get werewolves). The grandson will be raised by his vampire family and love them, but hate their evil/vampire ways and decide to take a different path and leave, knowing that if he stays he become just like his grandfather. I plan for him to find a home in Sulani working as a marine biologist. Sulani is the one place the vampires haven't taken since it's cut off from the outside world and so he will be able to be himself there and not live in his grandfather's dark shadow. Then perhaps he will catch the eye of a pretty mermaid, become a merman and have a merfamily and one of their children will want to leave the island to become part of the 'real world' and join their vampire relatives, and so the story goes on and on... I have lots of ideas, but nothing is set in stone. I just like to let my imagination run wild and see what feels right and the most fun.

Tell a story, create some drama, let them be players in other sim's lives.

I do wish there were storyline elements to the game, a bunch of scenarios in the style of the Strangerville mystery. (Progression through a story that is related to an element of the sims life, some based on careers, some on life stages, family events etc, cast some non- played sims as "actors" in the storylines and bam, we have more to do than aspire to wealth.

The only difference, to me, is that they don't have to do anything for money. Sometimes, I want a Sim to focus on honing a particular skill or child-rearing. Other times, I want them to play through a profession.