Unintentional glitches can add character to your painted furniture. Like chipping, peeling and cracking for example. Yes, you may want to weep at first, but consider that a lot of popular paint techniques started out this way!
(The striking dresser from www.petticoatjunktion.com above is a perfect example!)
Still, if you prefer a more reliable outcome - these are a few vital points:
1. PRIMING ~ NOT NECESSARY (but please read nr. 2)
2. SANDING ~ NOT NECESSARY - That said, some surfaces may need a light sand (eg. Melamine and similar super smooth blended surfaces) + a first thinned coat of chalkpaint (allowed to dry) before a second normal coat, for better results. Furniture previously treated with coatings containing silicones can repel paint.
Sand areas that are resisting the paint down, and you may also need to coat the area with a waterbased varnish to create a barrier, then repaint.
3. CLEANING ~ ALWAYS
You don't normally need to sand, strip or prime but CLEANING is always vital. As with any paint or coating, the surface about to be painted needs to be free of oil and grease - or it can affect your finish. Unless of course you, like me, enjoy that element of mystery and sometimes paint over dust as well as spiderwebs :)
Either by leeching through or resisting the paint. Use water and dishwashing liquid to wash and then dry your item.