No matter how careful a scientist is, lab equipment is bound to get dirty. Depending on the chemicals that are on the equipment and how the equipment is going to be used, cleaning protocols differ drastically. A good rule of thumb is to overclean instead of underclean, but always ensure that any cleaning chemicals will not interfere with future experiments using the equipment
Clean the equipment thoroughly with soap and water for basic cleaning. You may need to use a wire brush to remove some residue. Rinse with purified water to ensure that all soap residue is removed.
Boil purified water in the lab equipment to remove caked-on material like solidified agar or other gelatin-like products.
Rinse with acetone to remove traces of organic materials including soap residue.
Rinse with ethanol to sterilize any lab equipment that must have all bacteria and other microorganisms removed before use.
Rinse with an RNAse remover, such as RNAse Displace, if the equipment will be used in any DNA research, since RNAse can destroy your experiments.
If you are just cleaning standard lab equipment and it won't come clean, still try one of the other methods. Even if you don't care if it is sterile, acetone and ethanol will remove nearly anything that soap and water won't.
All of these chemicals are toxic, and most are flammable, so read and follow all safety precautions before use.