Your first best friend in identifying which clothes need dry cleaning is the clothing tags. Make sure to keep these on your clothes, or at least take note of any washing instructions if you find the tags too uncomfortable to keep. Store these instructions close to where you sort your laundry so you don’t lose them.
After wearing anything that calls for dry cleaning, allow it to air out for a few hours and inspect it for grime and odors. It may not be necessary to have them professionally cleaned after each wearing. Some low-priority jobs may simply call for a lint roller, clothing brush, or refresher spray before they are fresh and ready to wear again.
If your clothing has any complicated pleats or pin tucks, take care about trying to wash them by yourself. You may not be able to restore these without professional help. Most of these should be trusted to a proper dry cleaner.