There is a hard method which is tedious & time consuming.
Every sim day, go to Studiotown. 1st star requires you to sing on a
mini stage for other sims to enjoy for free Or bother the paparazzi
when your sim is in a good mood. He will take your photo & may
lead you to gain half a star. The rest you can figure out yourself.
Keep your sim happy & their performance has a greater chance of
being star-worthy.
There is also an easier method which requires you to have the
Sims 1 Makin Magic expansion pack. Learn to create the
celebrity charm and use it on the sim you want to be catapulted
into stardom.
This was 1 of my most fondest memories. My sim won so many Simmy
awards.
I read on the sim newspaper to check if my sim is the most top
rated sim in town.
I remember the fun times I had murdering my competiting
celebrities (NPCs) with fire.
My sim easily became the top sim celeb in my town. XD