Personally I only use waterproof mascara. I am always on the move and do not have time to stop and reapply makeup through the day. Plus I spend a lot of time in a hottub and have a side job that I usually end up sweating at not to mention the sudden urge to do soccer drills and the like. Plus waterproof mascara tends to last longer in the container.
Mascara is pretty straightforward. Remove the wand, get off the excess mascara and any clumps, and apply to your eyelashes. Do not pump the wand in and out of the container. Instead just insert it, twirl it, and then pull up. Remove the excess at that point.
However, not everyone has perfect eyelashes.
I start off using an eyebrow brush to seperate my lashes. On one eye, the lashes turn down so I will use an eyelash curler to correct it a bit. Never use the curler after applying the mascara as that can lead to eyelashes being pulled out.
Start from the base of the upper lashes and sweep outwards in a fluid motion, repeat as necessary to cover all of your upper eyelashes. On the bottom lashes you can either turn the wand so it is up and down and use just the tip to get the lashes or you can use the wand on the top part of the lashes in a motion like you used for your upper lashes.
Multiple coats can make your eyelashes look thicker but you need to let one coat dry before applying another. Good rule of thumb is to just do two or three coats, max. For work I stick with a single coat as my eyelashes are full and pretty dark as is. Clubbing I tend to go with three.
For mascara removal I use a bit of warm water splashed on and then a makeup removal/facial cleansing cloth like the kind Oil of Olay sells. I then rinse my face with cooler water and make sure I do not have any makeup on my face.
Odd spots for mascara: I use a clear mascara on my eyebrows after I am done with the rest of my face. It helps them maintain a definate shape and adds just a hint of shine for the first couple of hours.