Mono is called the "kissing disease" because it is carried in the saliva. If you kiss someone with mono, chances are you're gonna get it. This doesn't at all mean you HAVE to kiss them to get it... drinking from the same glass as an infected person is another way, or sharing utensils, or sipping from the same straw. So it's quite possible to get mono even if you're not intimate with anyone.
Cooties, on the other hand, are carried by girls. Methods of transmitting cooties known to third grader boys include touching a girl, talking to a girl, or even being looked at by a girl. The most significant symptom of cooties infection is merciless teasing by other boys on the playground. The best solution is to never have friendly contact with the girls... in fact, throwing dirtballs is great protection. If you do become infected the known cures are to make certain gestures (the 'cootie chant' thing recited by Gist), to recite the mantra 'Girls are stupid!', and if all that fails, hit any kid who mentions 'cooties' in your presence.