The cocci (singular coccus) are spherical, they are drawn as circles.
Bacilli (singular bacillus) are rod-shaped, drawn as lozenges.
Spirilli (singular spirillum) are spiral in shape.
Gram positive bacteria have a thick peptidoglycan layer which retains a crystal violet stain, so after Gram staining they appear purple down the microscope.
Gram negative bacteria have a thin peptidoglycan layer. Because of this, alcohol used in the procedure will wash the crystal violet out. The counterstaining with safranin stains the cells red. Gram negative bacteria have extra layers of lipopolysaccharide which protects the cells from lysozyme as well as the action of penicillin and other antibiotics.
The procedure for Gram stain in outline is as follows:
Heat fix a smear of bacteria
Stain using crystal violet stain
Fix the stain with iodine
Decolourise with alcohol
Counterstain with safranin.
When the cells are observed down the microscope Gram positive cells are purple in colour and Gram negative are red.
Bacteria culture
Petri dish or flask, given appropriate nutrients and conditions
Counts only live cells capable of reproducing (forming colonies) by transferring samples from serial dilution to agar plates and counting colonies after incubation
Multiply the number of counted colonies by the dilution factor and adjust for the volume plated to determine the number of bacteria in the original sample