To paint old furniture, start by preparing the surface: clean, sand, and prime. Choose your paint type (latex or oil-based), apply evenly, and allow it to dry completely before adding a second coat, says The Home Depot. You can also use chalk paint for a unique finish, according to Brewers Decorator Centres.
Detailed Steps:

Prepare the Space: Put down a drop cloth, remove any loose debris, and ensure good ventilation.

Clean the Furniture: Use sugar soap and a kitchen scrubber to clean the surface.
Sanding: Lightly sand the surface to help the paint adhere better.

Priming: Apply a primer, especially if it's an older piece or if you want to prevent paint from chipping, says Lick.
Choose Your Paint: Latex or oil-based paint for wood furniture, or consider chalk paint for a unique finish.

Apply the First Coat: Use a brush or roller (foam rollers are best for smooth surfaces) Allow to Dry: Follow the paint's drying time instructions before applying a second coat.
Second Coat: Apply a second coat for a more even finish.

Seal (Optional): For chalk paint, consider sealing with a clear wax or sealant for durability.

Maintenance: Clean regularly with a soft, damp cloth and protect with coasters.
Tips for a Smooth Finish:
Thin Coats: Apply thin layers of paint to avoid drips.  Work Downward: Start painting at the top and work downwards.

Sand Between Coats: Lightly sand with fine-grit sandpaper between coats to remove any imperfections.

Use a Tack Cloth: Clean with a tack cloth before applying each coat to remove dust.
Consider a Paint Sprayer: For a more professional finish, a spray paint can provide a smooth and even coat.